Difference between revisions of "Results of Incomplete Gamma and Related Functions"

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| [https://dlmf.nist.gov/8.2.E1 8.2.E1] || [[Item:Q2480|<math>\incgamma@{a}{z} = \int_{0}^{z}t^{a-1}e^{-t}\diff{t}</math>]] || <code>GAMMA(a)-GAMMA(a, z)= int((t)^(a - 1)* exp(- t), t = 0..z)</code> || <code>Gamma[a, 0, z]= Integrate[(t)^(a - 1)* Exp[- t], {t, 0, z}]</code> || Failure || Successful || Skip || -  
 
| [https://dlmf.nist.gov/8.2.E1 8.2.E1] || [[Item:Q2480|<math>\incgamma@{a}{z} = \int_{0}^{z}t^{a-1}e^{-t}\diff{t}</math>]] || <code>GAMMA(a)-GAMMA(a, z)= int((t)^(a - 1)* exp(- t), t = 0..z)</code> || <code>Gamma[a, 0, z]= Integrate[(t)^(a - 1)* Exp[- t], {t, 0, z}]</code> || Failure || Successful || Skip || -  
 
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| [https://dlmf.nist.gov/8.2.E2 8.2.E2] || [[Item:Q2481|<math>\incGamma@{a}{z} = \int_{z}^{\infty}t^{a-1}e^{-t}\diff{t}</math>]] || <code>GAMMA(a, z)= int((t)^(a - 1)* exp(- t), t = z..infinity)</code> || <code>Gamma[a, z]= Integrate[(t)^(a - 1)* Exp[- t], {t, z, Infinity}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[0, Or[Unequal[Im[z], 0], Greater[Re[z], 0]]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[0, Or[Unequal[Im[z], 0], Greater[Re[z], 0]]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[0, Or[Unequal[Im[z], 0], Greater[Re[z], 0]]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[0, Or[Unequal[Im[z], 0], Greater[Re[z], 0]]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
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| [https://dlmf.nist.gov/8.2.E2 8.2.E2] || [[Item:Q2481|<math>\incGamma@{a}{z} = \int_{z}^{\infty}t^{a-1}e^{-t}\diff{t}</math>]] || <code>GAMMA(a, z)= int((t)^(a - 1)* exp(- t), t = z..infinity)</code> || <code>Gamma[a, z]= Integrate[(t)^(a - 1)* Exp[- t], {t, z, Infinity}]</code> || Failure || Failure || Skip || Successful
 
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| [https://dlmf.nist.gov/8.2.E3 8.2.E3] || [[Item:Q2482|<math>\incgamma@{a}{z}+\incGamma@{a}{z} = \EulerGamma@{a}</math>]] || <code>GAMMA(a)-GAMMA(a, z)+ GAMMA(a, z)= GAMMA(a)</code> || <code>Gamma[a, 0, z]+ Gamma[a, z]= Gamma[a]</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/8.2.E3 8.2.E3] || [[Item:Q2482|<math>\incgamma@{a}{z}+\incGamma@{a}{z} = \EulerGamma@{a}</math>]] || <code>GAMMA(a)-GAMMA(a, z)+ GAMMA(a, z)= GAMMA(a)</code> || <code>Gamma[a, 0, z]+ Gamma[a, z]= Gamma[a]</code> || Successful || Successful || - || -  
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| [https://dlmf.nist.gov/8.2.E6 8.2.E6] || [[Item:Q2486|<math>\scincgamma@{a}{z} = z^{-a}\normincGammaP@{a}{z}</math>]] || <code>(z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a)= (z)^(- a)* (GAMMA(a)-GAMMA(a, z))/GAMMA(a)</code> || <code>Error</code> || Successful || Error || - || -  
 
| [https://dlmf.nist.gov/8.2.E6 8.2.E6] || [[Item:Q2486|<math>\scincgamma@{a}{z} = z^{-a}\normincGammaP@{a}{z}</math>]] || <code>(z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a)= (z)^(- a)* (GAMMA(a)-GAMMA(a, z))/GAMMA(a)</code> || <code>Error</code> || Successful || Error || - || -  
 
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| [https://dlmf.nist.gov/8.2.E6 8.2.E6] || [[Item:Q2486|<math>z^{-a}\normincGammaP@{a}{z} = \frac{z^{-a}}{\EulerGamma@{a}}\incgamma@{a}{z}</math>]] || <code>(z)^(- a)* (GAMMA(a)-GAMMA(a, z))/GAMMA(a)=((z)^(- a))/(GAMMA(a))*GAMMA(a)-GAMMA(a, z)</code> || <code>(z)^(- a)* GammaRegularized[a, 0, z]=Divide[(z)^(- a),Gamma[a]]*Gamma[a, 0, z]</code> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.3504429851+.4826856014*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.4474572306+.2704599710*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>23.62700226+82.69161801*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>3.420707652-13.57627439*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-.4474572306-.2704599710*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>.3504429851-.4826856014*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>3.420707652+13.57627439*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>23.62700226-82.69161801*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-.4343882366+.4808114998*I <- {a = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>.7194242296-.2247089431*I <- {a = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>29.01554215+20.00785694*I <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>8.087330677+3.05352968*I <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>.7194242296+.2247089431*I <- {a = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.4343882366-.4808114998*I <- {a = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>8.087330677-3.05352968*I <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>29.01554215-20.00785694*I <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || -  
+
| [https://dlmf.nist.gov/8.2.E6 8.2.E6] || [[Item:Q2486|<math>z^{-a}\normincGammaP@{a}{z} = \frac{z^{-a}}{\EulerGamma@{a}}\incgamma@{a}{z}</math>]] || <code>(z)^(- a)* (GAMMA(a)-GAMMA(a, z))/GAMMA(a)=((z)^(- a))/(GAMMA(a))*GAMMA(a)-GAMMA(a, z)</code> || <code>(z)^(- a)* GammaRegularized[a, 0, z]=Divide[(z)^(- a),Gamma[a]]*Gamma[a, 0, z]</code> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.3504429851+.4826856014*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.4474572306+.2704599710*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>23.62700226+82.69161801*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>3.420707652-13.57627439*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || -  
 
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| [https://dlmf.nist.gov/8.2.E7 8.2.E7] || [[Item:Q2487|<math>\scincgamma@{a}{z} = \frac{1}{\EulerGamma@{a}}\int_{0}^{1}t^{a-1}e^{-zt}\diff{t}</math>]] || <code>(z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a)=(1)/(GAMMA(a))*int((t)^(a - 1)* exp(- z*t), t = 0..1)</code> || <code>Error</code> || Failure || Error || Skip || -  
 
| [https://dlmf.nist.gov/8.2.E7 8.2.E7] || [[Item:Q2487|<math>\scincgamma@{a}{z} = \frac{1}{\EulerGamma@{a}}\int_{0}^{1}t^{a-1}e^{-zt}\diff{t}</math>]] || <code>(z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a)=(1)/(GAMMA(a))*int((t)^(a - 1)* exp(- z*t), t = 0..1)</code> || <code>Error</code> || Failure || Error || Skip || -  
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| [https://dlmf.nist.gov/8.2.E8 8.2.E8] || [[Item:Q2488|<math>\incgamma@{a}{ze^{2\pi mi}} = e^{2\pi mia}\incgamma@{a}{z}</math>]] || <code>GAMMA(a)-GAMMA(a, z*exp(2*Pi*m*I))= exp(2*Pi*m*I*a)*GAMMA(a)-GAMMA(a, z)</code> || <code>Gamma[a, 0, z*Exp[2*Pi*m*I]]= Exp[2*Pi*m*I*a]*Gamma[a, 0, z]</code> || Failure || Failure || Successful || Successful  
 
| [https://dlmf.nist.gov/8.2.E8 8.2.E8] || [[Item:Q2488|<math>\incgamma@{a}{ze^{2\pi mi}} = e^{2\pi mia}\incgamma@{a}{z}</math>]] || <code>GAMMA(a)-GAMMA(a, z*exp(2*Pi*m*I))= exp(2*Pi*m*I*a)*GAMMA(a)-GAMMA(a, z)</code> || <code>Gamma[a, 0, z*Exp[2*Pi*m*I]]= Exp[2*Pi*m*I*a]*Gamma[a, 0, z]</code> || Failure || Failure || Successful || Successful  
 
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| [https://dlmf.nist.gov/8.2.E9 8.2.E9] || [[Item:Q2489|<math>\incGamma@{a}{ze^{2\pi mi}} = e^{2\pi mia}\incGamma@{a}{z}+(1-e^{2\pi mia})\EulerGamma@{a}</math>]] || <code>GAMMA(a, z*exp(2*Pi*m*I))= exp(2*Pi*m*I*a)*GAMMA(a, z)+(1 - exp(2*Pi*m*I*a))* GAMMA(a)</code> || <code>Gamma[a, z*Exp[2*Pi*m*I]]= Exp[2*Pi*m*I*a]*Gamma[a, z]+(1 - Exp[2*Pi*m*I*a])* Gamma[a]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.2249049111-.4410511843e-1*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}</code><br><code>-.2248750758-.4411585330e-1*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}</code><br><code>-.2248750795-.4411584875e-1*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}</code><br><code>-1.005323136+.3326243216*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 1}</code><br><code>-1.005227386+.3325134381*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}</code><br><code>-1.005227403+.3325134619*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 3}</code><br><code>20.46249955+81.80630491*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), m = 1}</code><br><code>20.45425972+81.79804426*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), m = 2}</code><br><code>20.45426304+81.79804594*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), m = 3}</code><br><code>.1380013835-.6459749422e-1*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), m = 1}</code><br><code>.1379895862-.6458002320e-1*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), m = 2}</code><br><code>.1379895857-.6458002881e-1*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), m = 3}</code><br><code>-7470.619632+1666.547276*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}</code><br><code>40153142.99-38054433.76*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}</code><br><code>-.1078988446e12+.3850474280e12*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}</code><br><code>-1231.554386+1108.053850*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 1}</code><br><code>3527566.842-11442035.17*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}</code><br><code>.2056934222e11+.8406857680e11*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 3}</code><br><code>1095.761010-111.286886*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), m = 1}</code><br><code>-6383542.479+4755777.90*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), m = 2}</code><br><code>.2195519693e11-.531867945e11*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), m = 3}</code><br><code>-176581.1742-583404.7743*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), m = 1}</code><br><code>3259806629.+2963403529.*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), m = 2}</code><br><code>-.3121706485e14-.6288807466e13*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), m = 3}</code><br><code>-886.8142859+709.6704236*I <- {a = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}</code><br><code>8133491.718-1111438.055*I <- {a = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}</code><br><code>-.5457968751e11-.2328231394e11*I <- {a = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}</code><br><code>-528.9091261+529.9238978*I <- {a = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 1}</code><br><code>5246689.544-1324472.318*I <- {a = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}</code><br><code>-.3746185707e11-.1125006634e11*I <- {a = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 3}</code><br><code>-304.8330801+212.9937977*I <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), m = 1}</code><br><code>2680978.291-190090.9563*I <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), m = 2}</code><br><code>-.1733669117e11-8767812652.*I <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), m = 3}</code><br><code>89917.05184-32090.13160*I <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), m = 1}</code><br><code>-676770926.6-134574125.9*I <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), m = 2}</code><br><code>.3699038153e13+.3345802717e13*I <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), m = 3}</code><br><code>-.2516682505e-1-.1004755343*I <- {a = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}</code><br><code>-.2517097198e-1-.1004618178*I <- {a = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}</code><br><code>-.2517097030e-1-.1004618191*I <- {a = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}</code><br><code>-.5489674093e-1-.1472317109*I <- {a = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 1}</code><br><code>-.5490067857e-1-.1472103307*I <- {a = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}</code><br><code>-.5490067589e-1-.1472103348*I <- {a = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 3}</code><br><code>8.397046195+10.19508799*I <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), m = 1}</code><br><code>8.396773066+10.19328107*I <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), m = 2}</code><br><code>8.396773131+10.19328157*I <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), m = 3}</code><br><code>-.2106780493e-1-.4693492636e-1*I <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), m = 1}</code><br><code>-.2106863628e-1-.4692785756e-1*I <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), m = 2}</code><br><code>-.2106863591e-1-.4692785866e-1*I <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), m = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.22490491118791595, -0.04410511845656586] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.2248750764783257, -0.044115852492705915] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.22487507925834865, -0.04411584909968558] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0053231382729926, 0.33262432134470665] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.005227396849198, 0.3325134406545761] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0052274003428132, 0.33251346061799697] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[20.46249974605223, 81.80630516774626] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[20.454261145614897, 81.79804542060461] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[20.454262710305986, 81.79804581625109] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.1380013834196427, -0.06459749433701602] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.13798958572122355, -0.06458002518444685] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.13798958588146235, -0.06458002809630577] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7470.619644952175, 1666.5472729681096] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.015314239600219*^7, -3.80544338108609*^7] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0789884878496332*^11, 3.850474305928836*^11] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1231.5543888002394, 1108.0538497197144] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3527566.724421209, -1.1442035111005586*^7] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.0569341689661465*^10, 8.40685777040521*^10] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1095.7610116067235, -111.28688635268304] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6383542.3916354915, 4755777.914966784] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.195519752693039*^10, -5.318679484476776*^10] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-176581.17394191804, -583404.7761796014] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.2598066316560135*^9, 2.963403487390624*^9] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.1217065120398496*^13, -6.288807808095331*^12] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-886.8142851470194, 709.6704251919407] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8133491.655967515, -1111437.9869255058] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.457968815222714*^10, -2.3282313627352165*^10] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-528.9091257238363, 529.9238982674376] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5246689.508076388, -1324472.2648729375] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.7461857452533104*^10, -1.1250066115913736*^10] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-304.83307996021597, 212.99379800143396] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2680978.2695867238, -190090.93321141892] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.7336691377977974*^10, -8.767812573847723*^9] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[89917.05188669058, -32090.13194435204] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.767709209813998*^8, -1.34574128655497*^8] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.69903822299039*^12, 3.345802707953902*^12] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.025166825060855283, -0.10047553413197906] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.025170971837805013, -0.10046181764225634] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.025170970371447107, -0.1004618189763399] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.054896740794276436, -0.14723171098103593] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.05490067793941428, -0.1472103320317673] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.054900675953830975, -0.14721033429049477] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.397046195215205, 10.195088034511809] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.396773178420329, 10.193281301506214] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.396773082538449, 10.193281535405262] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.021067804958581127, -0.04693492633141024] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.021068636465505875, -0.046927857749596076] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.02106863586483843, -0.04692785852979759] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/8.2.E9 8.2.E9] || [[Item:Q2489|<math>\incGamma@{a}{ze^{2\pi mi}} = e^{2\pi mia}\incGamma@{a}{z}+(1-e^{2\pi mia})\EulerGamma@{a}</math>]] || <code>GAMMA(a, z*exp(2*Pi*m*I))= exp(2*Pi*m*I*a)*GAMMA(a, z)+(1 - exp(2*Pi*m*I*a))* GAMMA(a)</code> || <code>Gamma[a, z*Exp[2*Pi*m*I]]= Exp[2*Pi*m*I*a]*Gamma[a, z]+(1 - Exp[2*Pi*m*I*a])* Gamma[a]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.2249049111-.4410511843e-1*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}</code><br><code>-.2248750758-.4411585330e-1*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}</code><br><code>-.2248750795-.4411584875e-1*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}</code><br><code>-1.005323136+.3326243216*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.22490491118791595, -0.04410511845656586] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.2248750764783257, -0.044115852492705915] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.22487507925834865, -0.04411584909968558] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0053231382729926, 0.33262432134470665] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
| [https://dlmf.nist.gov/8.2.E10 8.2.E10] || [[Item:Q2490|<math>e^{-\pi ia}\incGamma@{a}{ze^{\pi i}}-e^{\pi ia}\incGamma@{a}{ze^{-\pi i}} = -\frac{2\pi i}{\EulerGamma@{1-a}}</math>]] || <code>exp(- Pi*I*a)*GAMMA(a, z*exp(Pi*I))- exp(Pi*I*a)*GAMMA(a, z*exp(- Pi*I))= -(2*Pi*I)/(GAMMA(1 - a))</code> || <code>Exp[- Pi*I*a]*Gamma[a, z*Exp[Pi*I]]- Exp[Pi*I*a]*Gamma[a, z*Exp[- Pi*I]]= -Divide[2*Pi*I,Gamma[1 - a]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-7167.292469-174.9289096*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>2.16987973+12.77160007*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>8.705606105-17.43270949*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-4.50134822-89.91653387*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-2.16987973+12.77160007*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>7167.292469-174.9289096*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>4.50134822-89.91653387*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-8.705606105-17.43270949*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>3.369439236+2.788984848*I <- {a = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-645.4110961-918.9294888*I <- {a = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>10.82304704+7.831702915*I <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>7.664340201+4.336898369*I <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>645.4110961-918.9294888*I <- {a = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-3.369439236+2.788984848*I <- {a = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-7.664340201+4.336898369*I <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-10.82304704+7.831702915*I <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-7167.2924809060105, -174.9289096706231] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.169879706441371, 12.771600034859095] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.70560609871773, -17.43270953363519] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.501348191090425, -89.91653394957189] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.169879706441371, 12.771600034859095] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7167.2924809060105, -174.9289096706231] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.501348191090425, -89.91653394957189] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-8.70560609871773, -17.43270953363519] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.369439241027149, 2.7889848429588855] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-645.4110982406346, -918.9294880188124] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.823047044974839, 7.831702902208898] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.664340200530641, 4.336898364261077] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[645.4110982406346, -918.9294880188124] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.369439241027149, 2.7889848429588855] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.664340200530641, 4.336898364261077] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-10.823047044974839, 7.831702902208898] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/8.2.E10 8.2.E10] || [[Item:Q2490|<math>e^{-\pi ia}\incGamma@{a}{ze^{\pi i}}-e^{\pi ia}\incGamma@{a}{ze^{-\pi i}} = -\frac{2\pi i}{\EulerGamma@{1-a}}</math>]] || <code>exp(- Pi*I*a)*GAMMA(a, z*exp(Pi*I))- exp(Pi*I*a)*GAMMA(a, z*exp(- Pi*I))= -(2*Pi*I)/(GAMMA(1 - a))</code> || <code>Exp[- Pi*I*a]*Gamma[a, z*Exp[Pi*I]]- Exp[Pi*I*a]*Gamma[a, z*Exp[- Pi*I]]= -Divide[2*Pi*I,Gamma[1 - a]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-7167.292469-174.9289096*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>2.16987973+12.77160007*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>8.705606105-17.43270949*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-4.50134822-89.91653387*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-7167.2924809060105, -174.9289096706231] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.169879706441371, 12.771600034859095] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.70560609871773, -17.43270953363519] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.501348191090425, -89.91653394957189] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
| [https://dlmf.nist.gov/8.2.E11 8.2.E11] || [[Item:Q2491|<math>\incGamma@{a}{ze^{+\pi i}} = \EulerGamma@{a}(1-z^{a}e^{+\pi ia}\scincgamma@{a}{-z})</math>]] || <code>GAMMA(a, z*exp(+ Pi*I))= GAMMA(a)*(1 - (z)^(a)* exp(+ Pi*I*a)*(- z)^(-(a))*(GAMMA(a)-GAMMA(a, - z))/GAMMA(a))</code> || <code>Error</code> || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>20.46249972+81.80630504*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.005323138+.3326243220*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>1095.761010-111.2868863*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-1231.554386+1108.053849*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-304.8330800+212.9937978*I <- {a = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-528.9091261+529.9238977*I <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>8.397046212+10.19508802*I <- {a = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.5489674088e-1-.1472317112*I <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || -  
+
| [https://dlmf.nist.gov/8.2.E11 8.2.E11] || [[Item:Q2491|<math>\incGamma@{a}{ze^{+\pi i}} = \EulerGamma@{a}(1-z^{a}e^{+\pi ia}\scincgamma@{a}{-z})</math>]] || <code>GAMMA(a, z*exp(+ Pi*I))= GAMMA(a)*(1 - (z)^(a)* exp(+ Pi*I*a)*(- z)^(-(a))*(GAMMA(a)-GAMMA(a, - z))/GAMMA(a))</code> || <code>Error</code> || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>20.46249972+81.80630504*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.005323138+.3326243220*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>1095.761010-111.2868863*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-1231.554386+1108.053849*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || -  
 
|-
 
|-
| [https://dlmf.nist.gov/8.2.E11 8.2.E11] || [[Item:Q2491|<math>\incGamma@{a}{ze^{-\pi i}} = \EulerGamma@{a}(1-z^{a}e^{-\pi ia}\scincgamma@{a}{-z})</math>]] || <code>GAMMA(a, z*exp(- Pi*I))= GAMMA(a)*(1 - (z)^(a)* exp(- Pi*I*a)*(- z)^(-(a))*(GAMMA(a)-GAMMA(a, - z))/GAMMA(a))</code> || <code>Error</code> || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1095.761010+111.2868863*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-1231.554386-1108.053849*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>20.46249972-81.80630504*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.005323138-.3326243220*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>8.397046212-10.19508802*I <- {a = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-.5489674088e-1+.1472317112*I <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-304.8330800-212.9937978*I <- {a = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-528.9091261-529.9238977*I <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br></div></div> || -  
+
| [https://dlmf.nist.gov/8.2.E11 8.2.E11] || [[Item:Q2491|<math>\incGamma@{a}{ze^{-\pi i}} = \EulerGamma@{a}(1-z^{a}e^{-\pi ia}\scincgamma@{a}{-z})</math>]] || <code>GAMMA(a, z*exp(- Pi*I))= GAMMA(a)*(1 - (z)^(a)* exp(- Pi*I*a)*(- z)^(-(a))*(GAMMA(a)-GAMMA(a, - z))/GAMMA(a))</code> || <code>Error</code> || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1095.761010+111.2868863*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-1231.554386-1108.053849*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>20.46249972-81.80630504*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.005323138-.3326243220*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || -  
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.2.E12 8.2.E12] || [[Item:Q2492|<math>\deriv[2]{w}{z}+\left(1+\frac{1-a}{z}\right)\deriv{w}{z} = 0</math>]] || <code>diff(w, [z$(2)])+(1 +(1 - a)/(z))* diff(w, z)= 0</code> || <code>D[w, {z, 2}]+(1 +Divide[1 - a,z])* D[w, z]= 0</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/8.2.E12 8.2.E12] || [[Item:Q2492|<math>\deriv[2]{w}{z}+\left(1+\frac{1-a}{z}\right)\deriv{w}{z} = 0</math>]] || <code>diff(w, [z$(2)])+(1 +(1 - a)/(z))* diff(w, z)= 0</code> || <code>D[w, {z, 2}]+(1 +Divide[1 - a,z])* D[w, z]= 0</code> || Successful || Successful || - || -  
 
|-
 
|-
| [https://dlmf.nist.gov/8.2.E13 8.2.E13] || [[Item:Q2493|<math>\deriv[2]{w}{z}-\left(1+\frac{1-a}{z}\right)\deriv{w}{z}+\frac{1-a}{z^{2}}w = 0</math>]] || <code>diff(w, [z$(2)])-(1 +(1 - a)/(z))* diff(w, z)+(1 - a)/((z)^(2))*w = 0</code> || <code>D[w, {z, 2}]-(1 +Divide[1 - a,z])* D[w, z]+Divide[1 - a,(z)^(2)]*w = 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.6464466093-.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>.6464466093+.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-.6464466093-.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>.6464466093+.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-.3535533907+.6464466093*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>.3535533907-.6464466093*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-.3535533907+.6464466093*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>.3535533907-.6464466093*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>.6464466093+.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.6464466093-.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>.6464466093+.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.6464466093-.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>.3535533907-.6464466093*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.3535533907+.6464466093*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>.3535533907-.6464466093*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.3535533907+.6464466093*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>.3535533907+.6464466093*I <- {a = 2^(1/2)-I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.3535533907-.6464466093*I <- {a = 2^(1/2)-I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>.3535533907+.6464466093*I <- {a = 2^(1/2)-I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.3535533907-.6464466093*I <- {a = 2^(1/2)-I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>.6464466093-.3535533907*I <- {a = 2^(1/2)-I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.6464466093+.3535533907*I <- {a = 2^(1/2)-I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>.6464466093-.3535533907*I <- {a = 2^(1/2)-I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.6464466093+.3535533907*I <- {a = 2^(1/2)-I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-.3535533907-.6464466093*I <- {a = 2^(1/2)-I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>.3535533907+.6464466093*I <- {a = 2^(1/2)-I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-.3535533907-.6464466093*I <- {a = 2^(1/2)-I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>.3535533907+.6464466093*I <- {a = 2^(1/2)-I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-.6464466093+.3535533907*I <- {a = 2^(1/2)-I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>.6464466093-.3535533907*I <- {a = 2^(1/2)-I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-.6464466093+.3535533907*I <- {a = 2^(1/2)-I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>.6464466093-.3535533907*I <- {a = 2^(1/2)-I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>1.353553391-.3535533907*I <- {a = -2^(1/2)-I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.353553391+.3535533907*I <- {a = -2^(1/2)-I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>1.353553391-.3535533907*I <- {a = -2^(1/2)-I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.353553391+.3535533907*I <- {a = -2^(1/2)-I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-.3535533907-1.353553391*I <- {a = -2^(1/2)-I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>.3535533907+1.353553391*I <- {a = -2^(1/2)-I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-.3535533907-1.353553391*I <- {a = -2^(1/2)-I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>.3535533907+1.353553391*I <- {a = -2^(1/2)-I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-1.353553391+.3535533907*I <- {a = -2^(1/2)-I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>1.353553391-.3535533907*I <- {a = -2^(1/2)-I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.353553391+.3535533907*I <- {a = -2^(1/2)-I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>1.353553391-.3535533907*I <- {a = -2^(1/2)-I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>.3535533907+1.353553391*I <- {a = -2^(1/2)-I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.3535533907-1.353553391*I <- {a = -2^(1/2)-I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>.3535533907+1.353553391*I <- {a = -2^(1/2)-I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.3535533907-1.353553391*I <- {a = -2^(1/2)-I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>.3535533907-1.353553391*I <- {a = -2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.3535533907+1.353553391*I <- {a = -2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>.3535533907-1.353553391*I <- {a = -2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.3535533907+1.353553391*I <- {a = -2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-1.353553391-.3535533907*I <- {a = -2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>1.353553391+.3535533907*I <- {a = -2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.353553391-.3535533907*I <- {a = -2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>1.353553391+.3535533907*I <- {a = -2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-.3535533907+1.353553391*I <- {a = -2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>.3535533907-1.353553391*I <- {a = -2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-.3535533907+1.353553391*I <- {a = -2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>.3535533907-1.353553391*I <- {a = -2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>1.353553391+.3535533907*I <- {a = -2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.353553391-.3535533907*I <- {a = -2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>1.353553391+.3535533907*I <- {a = -2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.353553391-.3535533907*I <- {a = -2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.6464466094067263, -0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6464466094067263, 0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6464466094067263, -0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6464466094067263, 0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.35355339059327373, 0.6464466094067263] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.35355339059327373, -0.6464466094067263] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.35355339059327373, 0.6464466094067263] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.35355339059327373, -0.6464466094067263] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6464466094067263, 0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6464466094067263, -0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6464466094067263, 0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6464466094067263, -0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.35355339059327373, -0.6464466094067263] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.35355339059327373, 0.6464466094067263] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.35355339059327373, -0.6464466094067263] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.35355339059327373, 0.6464466094067263] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.35355339059327373, 0.6464466094067263] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.35355339059327373, -0.6464466094067263] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.35355339059327373, 0.6464466094067263] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.35355339059327373, -0.6464466094067263] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6464466094067263, -0.35355339059327373] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6464466094067263, 0.35355339059327373] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6464466094067263, -0.35355339059327373] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6464466094067263, 0.35355339059327373] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.35355339059327373, -0.6464466094067263] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.35355339059327373, 0.6464466094067263] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.35355339059327373, -0.6464466094067263] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.35355339059327373, 0.6464466094067263] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6464466094067263, 0.35355339059327373] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6464466094067263, -0.35355339059327373] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6464466094067263, 0.35355339059327373] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6464466094067263, -0.35355339059327373] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3535533905932735, -0.3535533905932736] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.3535533905932735, 0.3535533905932736] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3535533905932735, -0.3535533905932736] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.3535533905932735, 0.3535533905932736] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3535533905932736, -1.3535533905932735] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3535533905932736, 1.3535533905932735] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3535533905932736, -1.3535533905932735] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3535533905932736, 1.3535533905932735] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.3535533905932735, 0.3535533905932736] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3535533905932735, -0.3535533905932736] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.3535533905932735, 0.3535533905932736] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3535533905932735, -0.3535533905932736] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3535533905932736, 1.3535533905932735] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3535533905932736, -1.3535533905932735] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3535533905932736, 1.3535533905932735] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3535533905932736, -1.3535533905932735] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3535533905932736, -1.3535533905932735] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3535533905932736, 1.3535533905932735] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3535533905932736, -1.3535533905932735] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3535533905932736, 1.3535533905932735] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.3535533905932735, -0.3535533905932736] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3535533905932735, 0.3535533905932736] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.3535533905932735, -0.3535533905932736] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3535533905932735, 0.3535533905932736] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3535533905932736, 1.3535533905932735] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3535533905932736, -1.3535533905932735] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3535533905932736, 1.3535533905932735] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3535533905932736, -1.3535533905932735] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3535533905932735, 0.3535533905932736] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.3535533905932735, -0.3535533905932736] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3535533905932735, 0.3535533905932736] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.3535533905932735, -0.3535533905932736] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/8.2.E13 8.2.E13] || [[Item:Q2493|<math>\deriv[2]{w}{z}-\left(1+\frac{1-a}{z}\right)\deriv{w}{z}+\frac{1-a}{z^{2}}w = 0</math>]] || <code>diff(w, [z$(2)])-(1 +(1 - a)/(z))* diff(w, z)+(1 - a)/((z)^(2))*w = 0</code> || <code>D[w, {z, 2}]-(1 +Divide[1 - a,z])* D[w, z]+Divide[1 - a,(z)^(2)]*w = 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.6464466093-.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>.6464466093+.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-.6464466093-.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>.6464466093+.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.6464466094067263, -0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6464466094067263, 0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6464466094067263, -0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6464466094067263, 0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.2.E14 8.2.E14] || [[Item:Q2494|<math>z\deriv[2]{\scincgamma}{z}+(a+1+z)\deriv{\scincgamma}{z}+a\scincgamma = 0</math>]] || <code>z*diff((+)^(-(z))*(GAMMA(z)-GAMMA(z, +))/GAMMA(z), [(a + 1 + z)*$(2)])*diff((+)^(-(z))*(GAMMA(z)-GAMMA(z, +))/GAMMA(z), a)*(0)^(-(=))*(GAMMA(=)-GAMMA(=, 0))/GAMMA(=)</code> || <code>Error</code> || Error || Error || - || -  
 
| [https://dlmf.nist.gov/8.2.E14 8.2.E14] || [[Item:Q2494|<math>z\deriv[2]{\scincgamma}{z}+(a+1+z)\deriv{\scincgamma}{z}+a\scincgamma = 0</math>]] || <code>z*diff((+)^(-(z))*(GAMMA(z)-GAMMA(z, +))/GAMMA(z), [(a + 1 + z)*$(2)])*diff((+)^(-(z))*(GAMMA(z)-GAMMA(z, +))/GAMMA(z), a)*(0)^(-(=))*(GAMMA(=)-GAMMA(=, 0))/GAMMA(=)</code> || <code>Error</code> || Error || Error || - || -  
Line 45: Line 45:
 
| [https://dlmf.nist.gov/8.4.E3 8.4.E3] || [[Item:Q2497|<math>\scincgamma@{\tfrac{1}{2}}{-z^{2}} = \frac{2e^{z^{2}}}{z\sqrt{\pi}}\DawsonsintF@{z}</math>]] || <code>(- (z)^(2))^(-((1)/(2)))*(GAMMA((1)/(2))-GAMMA((1)/(2), - (z)^(2)))/GAMMA((1)/(2))=(2*exp((z)^(2)))/(z*sqrt(Pi))*dawson(z)</code> || <code>Error</code> || Successful || Error || - || -  
 
| [https://dlmf.nist.gov/8.4.E3 8.4.E3] || [[Item:Q2497|<math>\scincgamma@{\tfrac{1}{2}}{-z^{2}} = \frac{2e^{z^{2}}}{z\sqrt{\pi}}\DawsonsintF@{z}</math>]] || <code>(- (z)^(2))^(-((1)/(2)))*(GAMMA((1)/(2))-GAMMA((1)/(2), - (z)^(2)))/GAMMA((1)/(2))=(2*exp((z)^(2)))/(z*sqrt(Pi))*dawson(z)</code> || <code>Error</code> || Successful || Error || - || -  
 
|-
 
|-
| [https://dlmf.nist.gov/8.4.E4 8.4.E4] || [[Item:Q2498|<math>\incGamma@{0}{z} = \int_{z}^{\infty}t^{-1}e^{-t}\diff{t}</math>]] || <code>GAMMA(0, z)= int((t)^(- 1)* exp(- t), t = z..infinity)</code> || <code>Gamma[0, z]= Integrate[(t)^(- 1)* Exp[- t], {t, z, Infinity}]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[0, And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[0, And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[0, And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[0, And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
+
| [https://dlmf.nist.gov/8.4.E4 8.4.E4] || [[Item:Q2498|<math>\incGamma@{0}{z} = \int_{z}^{\infty}t^{-1}e^{-t}\diff{t}</math>]] || <code>GAMMA(0, z)= int((t)^(- 1)* exp(- t), t = z..infinity)</code> || <code>Gamma[0, z]= Integrate[(t)^(- 1)* Exp[- t], {t, z, Infinity}]</code> || Successful || Failure || - || Successful
 
|-
 
|-
| [https://dlmf.nist.gov/8.4.E4 8.4.E4] || [[Item:Q2498|<math>\int_{z}^{\infty}t^{-1}e^{-t}\diff{t} = \expintE@{z}</math>]] || <code>int((t)^(- 1)* exp(- t), t = z..infinity)= Ei(z)</code> || <code>Integrate[(t)^(- 1)* Exp[- t], {t, z, Infinity}]= -ExpIntegralEi[-(z)]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[Plus[ExpIntegralEi[Times[-1, z]], Gamma[0, z]], And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[Plus[ExpIntegralEi[Times[-1, z]], Gamma[0, z]], And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[Plus[ExpIntegralEi[Times[-1, z]], Gamma[0, z]], And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[Plus[ExpIntegralEi[Times[-1, z]], Gamma[0, z]], And[Greater[Re[z], 0], Equal[Im[z], 0]]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
+
| [https://dlmf.nist.gov/8.4.E4 8.4.E4] || [[Item:Q2498|<math>\int_{z}^{\infty}t^{-1}e^{-t}\diff{t} = \expintE@{z}</math>]] || <code>int((t)^(- 1)* exp(- t), t = z..infinity)= Ei(z)</code> || <code>Integrate[(t)^(- 1)* Exp[- t], {t, z, Infinity}]= -ExpIntegralEi[-(z)]</code> || Failure || Failure || Skip || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.4.E5 8.4.E5] || [[Item:Q2499|<math>\incGamma@{1}{z} = e^{-z}</math>]] || <code>GAMMA(1, z)= exp(- z)</code> || <code>Gamma[1, z]= Exp[- z]</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/8.4.E5 8.4.E5] || [[Item:Q2499|<math>\incGamma@{1}{z} = e^{-z}</math>]] || <code>GAMMA(1, z)= exp(- z)</code> || <code>Gamma[1, z]= Exp[- z]</code> || Successful || Successful || - || -  
Line 63: Line 63:
 
| [https://dlmf.nist.gov/8.4.E10 8.4.E10] || [[Item:Q2504|<math>\normincGammaQ@{n+1}{z} = e^{-z}e_{n}(z)</math>]] || <code>GAMMA(n + 1, z)/GAMMA(n + 1)= exp(- z)*exp(1)[n]*(z)</code> || <code>GammaRegularized[n + 1, z]= Exp[- z]*Subscript[E, n]*(z)</code> || Failure || Failure || Error || Successful  
 
| [https://dlmf.nist.gov/8.4.E10 8.4.E10] || [[Item:Q2504|<math>\normincGammaQ@{n+1}{z} = e^{-z}e_{n}(z)</math>]] || <code>GAMMA(n + 1, z)/GAMMA(n + 1)= exp(- z)*exp(1)[n]*(z)</code> || <code>GammaRegularized[n + 1, z]= Exp[- z]*Subscript[E, n]*(z)</code> || Failure || Failure || Error || Successful  
 
|-
 
|-
| [https://dlmf.nist.gov/8.4.E12 8.4.E12] || [[Item:Q2506|<math>\scincgamma@{-n}{z} = z^{n}</math>]] || <code>(z)^(-(- n))*(GAMMA(- n)-GAMMA(- n, z))/GAMMA(- n)= (z)^(n)</code> || <code>Error</code> || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)+I*2^(1/2), n = 1}</code><br><code>Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)+I*2^(1/2), n = 2}</code><br><code>Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)+I*2^(1/2), n = 3}</code><br><code>Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)-I*2^(1/2), n = 1}</code><br><code>Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)-I*2^(1/2), n = 2}</code><br><code>Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)-I*2^(1/2), n = 3}</code><br><code>Float(undefined)+Float(undefined)*I <- {z = -2^(1/2)-I*2^(1/2), n = 1}</code><br><code>Float(undefined)+Float(undefined)*I <- {z = -2^(1/2)-I*2^(1/2), n = 2}</code><br><code>Float(undefined)+Float(undefined)*I <- {z = -2^(1/2)-I*2^(1/2), n = 3}</code><br><code>Float(undefined)+Float(undefined)*I <- {z = -2^(1/2)+I*2^(1/2), n = 1}</code><br><code>Float(undefined)+Float(undefined)*I <- {z = -2^(1/2)+I*2^(1/2), n = 2}</code><br><code>Float(undefined)+Float(undefined)*I <- {z = -2^(1/2)+I*2^(1/2), n = 3}</code><br></div></div> || -  
+
| [https://dlmf.nist.gov/8.4.E12 8.4.E12] || [[Item:Q2506|<math>\scincgamma@{-n}{z} = z^{n}</math>]] || <code>(z)^(-(- n))*(GAMMA(- n)-GAMMA(- n, z))/GAMMA(- n)= (z)^(n)</code> || <code>Error</code> || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)+I*2^(1/2), n = 1}</code><br><code>Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)+I*2^(1/2), n = 2}</code><br><code>Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)+I*2^(1/2), n = 3}</code><br><code>Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)-I*2^(1/2), n = 1}</code><br>... skip entries to safe data<br></div></div> || -  
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.4.E13 8.4.E13] || [[Item:Q2507|<math>\incGamma@{1-n}{z} = z^{1-n}\genexpintE{n}@{z}</math>]] || <code>GAMMA(1 - n, z)= (z)^(1 - n)* Ei(n, z)</code> || <code>Gamma[1 - n, z]= (z)^(1 - n)* ExpIntegralE[n, z]</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/8.4.E13 8.4.E13] || [[Item:Q2507|<math>\incGamma@{1-n}{z} = z^{1-n}\genexpintE{n}@{z}</math>]] || <code>GAMMA(1 - n, z)= (z)^(1 - n)* Ei(n, z)</code> || <code>Gamma[1 - n, z]= (z)^(1 - n)* ExpIntegralE[n, z]</code> || Successful || Successful || - || -  
 
|-
 
|-
| [https://dlmf.nist.gov/8.4.E14 8.4.E14] || [[Item:Q2508|<math>\normincGammaQ@{n+\tfrac{1}{2}}{z^{2}} = \erfc@{z}+\frac{e^{-z^{2}}}{\sqrt{\pi}}\sum_{k=1}^{n}\frac{z^{2k-1}}{\Pochhammersym{\tfrac{1}{2}}{k}}</math>]] || <code>GAMMA(n +(1)/(2), (z)^(2))/GAMMA(n +(1)/(2))= erfc(z)+(exp(- (z)^(2)))/(sqrt(Pi))*sum(((z)^(2*k - 1))/(pochhammer((1)/(2), k)), k = 1..n)</code> || <code>GammaRegularized[n +Divide[1,2], (z)^(2)]= Erfc[z]+Divide[Exp[- (z)^(2)],Sqrt[Pi]]*Sum[Divide[(z)^(2*k - 1),Pochhammer[Divide[1,2], k]], {k, 1, n}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-6.522116143801526, 0.8770870118427658] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.400077458243353, -11.126893574158686] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.80629147935897, -12.531631677265604] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.522116143801526, -0.8770870118427658] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.400077458243353, 11.126893574158686] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.806291479358972, 12.531631677265604] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/8.4.E14 8.4.E14] || [[Item:Q2508|<math>\normincGammaQ@{n+\tfrac{1}{2}}{z^{2}} = \erfc@{z}+\frac{e^{-z^{2}}}{\sqrt{\pi}}\sum_{k=1}^{n}\frac{z^{2k-1}}{\Pochhammersym{\tfrac{1}{2}}{k}}</math>]] || <code>GAMMA(n +(1)/(2), (z)^(2))/GAMMA(n +(1)/(2))= erfc(z)+(exp(- (z)^(2)))/(sqrt(Pi))*sum(((z)^(2*k - 1))/(pochhammer((1)/(2), k)), k = 1..n)</code> || <code>GammaRegularized[n +Divide[1,2], (z)^(2)]= Erfc[z]+Divide[Exp[- (z)^(2)],Sqrt[Pi]]*Sum[Divide[(z)^(2*k - 1),Pochhammer[Divide[1,2], k]], {k, 1, n}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-6.522116143801526, 0.8770870118427658] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.400077458243353, -11.126893574158686] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.80629147935897, -12.531631677265604] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.522116143801526, -0.8770870118427658] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
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| [https://dlmf.nist.gov/8.4.E15 8.4.E15] || [[Item:Q2509|<math>\incGamma@{-n}{z} = \frac{(-1)^{n}}{n!}\left(\expintE@{z}-e^{-z}\sum_{k=0}^{n-1}\frac{(-1)^{k}k!}{z^{k+1}}\right)</math>]] || <code>GAMMA(- n, z)=((- 1)^(n))/(factorial(n))*(Ei(z)- exp(- z)*sum(((- 1)^(k)* factorial(k))/((z)^(k + 1)), k = 0..n - 1))</code> || <code>Gamma[- n, z]=Divide[(- 1)^(n),(n)!]*(-ExpIntegralEi[-(z)]- Exp[- z]*Sum[Divide[(- 1)^(k)* (k)!,(z)^(k + 1)], {k, 0, n - 1}])</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.3877787807814457*^-17, 3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.734723475976807*^-18, -1.5707963267948966] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.3368086899420177*^-19, 0.5235987755982987] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3877787807814457*^-17, -3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.734723475976807*^-18, 1.5707963267948966] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.3368086899420177*^-19, -0.5235987755982987] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.220446049250313*^-16, -3.1415926535897936] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.551115123125783*^-17, 1.5707963267948966] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-8.326672684688674*^-17, -0.5235987755982988] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.220446049250313*^-16, 3.1415926535897936] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.551115123125783*^-17, -1.5707963267948966] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-8.326672684688674*^-17, 0.5235987755982988] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/8.4.E15 8.4.E15] || [[Item:Q2509|<math>\incGamma@{-n}{z} = \frac{(-1)^{n}}{n!}\left(\expintE@{z}-e^{-z}\sum_{k=0}^{n-1}\frac{(-1)^{k}k!}{z^{k+1}}\right)</math>]] || <code>GAMMA(- n, z)=((- 1)^(n))/(factorial(n))*(Ei(z)- exp(- z)*sum(((- 1)^(k)* factorial(k))/((z)^(k + 1)), k = 0..n - 1))</code> || <code>Gamma[- n, z]=Divide[(- 1)^(n),(n)!]*(-ExpIntegralEi[-(z)]- Exp[- z]*Sum[Divide[(- 1)^(k)* (k)!,(z)^(k + 1)], {k, 0, n - 1}])</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.3877787807814457*^-17, 3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.734723475976807*^-18, -1.5707963267948966] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.3368086899420177*^-19, 0.5235987755982987] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3877787807814457*^-17, -3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.5.E1 8.5.E1] || [[Item:Q2510|<math>\incgamma@{a}{z} = a^{-1}z^{a}e^{-z}\KummerconfhyperM@{1}{1+a}{z}</math>]] || <code>GAMMA(a)-GAMMA(a, z)= (a)^(- 1)* (z)^(a)* exp(- z)*KummerM(1, 1 + a, z)</code> || <code>Gamma[a, 0, z]= (a)^(- 1)* (z)^(a)* Exp[- z]*Hypergeometric1F1[1, 1 + a, z]</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/8.5.E1 8.5.E1] || [[Item:Q2510|<math>\incgamma@{a}{z} = a^{-1}z^{a}e^{-z}\KummerconfhyperM@{1}{1+a}{z}</math>]] || <code>GAMMA(a)-GAMMA(a, z)= (a)^(- 1)* (z)^(a)* exp(- z)*KummerM(1, 1 + a, z)</code> || <code>Gamma[a, 0, z]= (a)^(- 1)* (z)^(a)* Exp[- z]*Hypergeometric1F1[1, 1 + a, z]</code> || Successful || Successful || - || -  
Line 91: Line 91:
 
| [https://dlmf.nist.gov/8.6.E2 8.6.E2] || [[Item:Q2516|<math>\incgamma@{a}{z} = z^{\frac{1}{2}a}\int_{0}^{\infty}e^{-t}t^{\frac{1}{2}a-1}\BesselJ{a}@{2\sqrt{zt}}\diff{t}</math>]] || <code>GAMMA(a)-GAMMA(a, z)= (z)^((1)/(2)*a)* int(exp(- t)*(t)^((1)/(2)*a - 1)* BesselJ(a, 2*sqrt(z*t)), t = 0..infinity)</code> || <code>Gamma[a, 0, z]= (z)^(Divide[1,2]*a)* Integrate[Exp[- t]*(t)^(Divide[1,2]*a - 1)* BesselJ[a, 2*Sqrt[z*t]], {t, 0, Infinity}]</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/8.6.E2 8.6.E2] || [[Item:Q2516|<math>\incgamma@{a}{z} = z^{\frac{1}{2}a}\int_{0}^{\infty}e^{-t}t^{\frac{1}{2}a-1}\BesselJ{a}@{2\sqrt{zt}}\diff{t}</math>]] || <code>GAMMA(a)-GAMMA(a, z)= (z)^((1)/(2)*a)* int(exp(- t)*(t)^((1)/(2)*a - 1)* BesselJ(a, 2*sqrt(z*t)), t = 0..infinity)</code> || <code>Gamma[a, 0, z]= (z)^(Divide[1,2]*a)* Integrate[Exp[- t]*(t)^(Divide[1,2]*a - 1)* BesselJ[a, 2*Sqrt[z*t]], {t, 0, Infinity}]</code> || Failure || Failure || Skip || Error  
 
|-
 
|-
| [https://dlmf.nist.gov/8.6.E3 8.6.E3] || [[Item:Q2517|<math>\incgamma@{a}{z} = z^{a}\int_{0}^{\infty}\exp@{-at-ze^{-t}}\diff{t}</math>]] || <code>GAMMA(a)-GAMMA(a, z)= (z)^(a)* int(exp(- a*t - z*exp(- t)), t = 0..infinity)</code> || <code>Gamma[a, 0, z]= (z)^(a)* Integrate[Exp[- a*t - z*Exp[- t]], {t, 0, Infinity}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[a, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[-1, Gamma[a]], Gamma[a, z], Gamma[a, 0, z]], Greater[Re[a], 0]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[a, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[-1, Gamma[a]], Gamma[a, z], Gamma[a, 0, z]], Greater[Re[a], 0]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[a, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[-1, Gamma[a]], Gamma[a, z], Gamma[a, 0, z]], Greater[Re[a], 0]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[a, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[-1, Gamma[a]], Gamma[a, z], Gamma[a, 0, z]], Greater[Re[a], 0]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
+
| [https://dlmf.nist.gov/8.6.E3 8.6.E3] || [[Item:Q2517|<math>\incgamma@{a}{z} = z^{a}\int_{0}^{\infty}\exp@{-at-ze^{-t}}\diff{t}</math>]] || <code>GAMMA(a)-GAMMA(a, z)= (z)^(a)* int(exp(- a*t - z*exp(- t)), t = 0..infinity)</code> || <code>Gamma[a, 0, z]= (z)^(a)* Integrate[Exp[- a*t - z*Exp[- t]], {t, 0, Infinity}]</code> || Failure || Failure || Skip || Successful
 
|-
 
|-
| [https://dlmf.nist.gov/8.6.E4 8.6.E4] || [[Item:Q2518|<math>\incGamma@{a}{z} = \frac{z^{a}e^{-z}}{\EulerGamma@{1-a}}\int_{0}^{\infty}\frac{t^{-a}e^{-t}}{z+t}\diff{t}</math>]] || <code>GAMMA(a, z)=((z)^(a)* exp(- z))/(GAMMA(1 - a))*int(((t)^(- a)* exp(- t))/(z + t), t = 0..infinity)</code> || <code>Gamma[a, z]=Divide[(z)^(a)* Exp[- z],Gamma[1 - a]]*Integrate[Divide[(t)^(- a)* Exp[- t],z + t], {t, 0, Infinity}]</code> || Failure || Failure || Skip || Skip
+
| [https://dlmf.nist.gov/8.6.E4 8.6.E4] || [[Item:Q2518|<math>\incGamma@{a}{z} = \frac{z^{a}e^{-z}}{\EulerGamma@{1-a}}\int_{0}^{\infty}\frac{t^{-a}e^{-t}}{z+t}\diff{t}</math>]] || <code>GAMMA(a, z)=((z)^(a)* exp(- z))/(GAMMA(1 - a))*int(((t)^(- a)* exp(- t))/(z + t), t = 0..infinity)</code> || <code>Gamma[a, z]=Divide[(z)^(a)* Exp[- z],Gamma[1 - a]]*Integrate[Divide[(t)^(- a)* Exp[- t],z + t], {t, 0, Infinity}]</code> || Failure || Failure || Skip || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.6.E5 8.6.E5] || [[Item:Q2519|<math>\incGamma@{a}{z} = z^{a}e^{-z}\int_{0}^{\infty}\frac{e^{-zt}}{(1+t)^{1-a}}\diff{t}</math>]] || <code>GAMMA(a, z)= (z)^(a)* exp(- z)*int((exp(- z*t))/((1 + t)^(1 - a)), t = 0..infinity)</code> || <code>Gamma[a, z]= (z)^(a)* Exp[- z]*Integrate[Divide[Exp[- z*t],(1 + t)^(1 - a)], {t, 0, Infinity}]</code> || Successful || Failure || - || Error  
 
| [https://dlmf.nist.gov/8.6.E5 8.6.E5] || [[Item:Q2519|<math>\incGamma@{a}{z} = z^{a}e^{-z}\int_{0}^{\infty}\frac{e^{-zt}}{(1+t)^{1-a}}\diff{t}</math>]] || <code>GAMMA(a, z)= (z)^(a)* exp(- z)*int((exp(- z*t))/((1 + t)^(1 - a)), t = 0..infinity)</code> || <code>Gamma[a, z]= (z)^(a)* Exp[- z]*Integrate[Divide[Exp[- z*t],(1 + t)^(1 - a)], {t, 0, Infinity}]</code> || Successful || Failure || - || Error  
Line 121: Line 121:
 
| [https://dlmf.nist.gov/8.7.E3 8.7.E3] || [[Item:Q2529|<math>\EulerGamma@{a}-\sum_{k=0}^{\infty}\frac{(-1)^{k}z^{a+k}}{k!(a+k)} = \EulerGamma@{a}\left(1-z^{a}e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\EulerGamma@{a+k+1}}\right)</math>]] || <code>GAMMA(a)- sum(((- 1)^(k)* (z)^(a + k))/(factorial(k)*(a + k)), k = 0..infinity)= GAMMA(a)*(1 - (z)^(a)* exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..infinity))</code> || <code>Gamma[a]- Sum[Divide[(- 1)^(k)* (z)^(a + k),(k)!*(a + k)], {k, 0, Infinity}]= Gamma[a]*(1 - (z)^(a)* Exp[- z]*Sum[Divide[(z)^(k),Gamma[a + k + 1]], {k, 0, Infinity}])</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/8.7.E3 8.7.E3] || [[Item:Q2529|<math>\EulerGamma@{a}-\sum_{k=0}^{\infty}\frac{(-1)^{k}z^{a+k}}{k!(a+k)} = \EulerGamma@{a}\left(1-z^{a}e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\EulerGamma@{a+k+1}}\right)</math>]] || <code>GAMMA(a)- sum(((- 1)^(k)* (z)^(a + k))/(factorial(k)*(a + k)), k = 0..infinity)= GAMMA(a)*(1 - (z)^(a)* exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..infinity))</code> || <code>Gamma[a]- Sum[Divide[(- 1)^(k)* (z)^(a + k),(k)!*(a + k)], {k, 0, Infinity}]= Gamma[a]*(1 - (z)^(a)* Exp[- z]*Sum[Divide[(z)^(k),Gamma[a + k + 1]], {k, 0, Infinity}])</code> || Successful || Successful || - || -  
 
|-
 
|-
| [https://dlmf.nist.gov/8.8.E1 8.8.E1] || [[Item:Q2533|<math>\incgamma@{a+1}{z} = a\incgamma@{a}{z}-z^{a}e^{-z}</math>]] || <code>GAMMA(a + 1)-GAMMA(a + 1, z)= a*GAMMA(a)-GAMMA(a, z)- (z)^(a)* exp(- z)</code> || <code>Gamma[a + 1, 0, z]= a*Gamma[a, 0, z]- (z)^(a)* Exp[- z]</code> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.135004907e-1-.2375774782*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>.8693672828+.710002389*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>107.1902160-63.3824277*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.1657436948-.7422690683*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>.8693672828-.710002389*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>.135004907e-1+.2375774782*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-.1657436948+.7422690683*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>107.1902160+63.3824277*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-.1520611888+.9119148087e-1*I <- {a = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.1417494577e-1+.2037473416e-1*I <- {a = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>.7143741874e-1-.1030661023*I <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>34.87574808-12.92049251*I <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-.1417494577e-1-.2037473416e-1*I <- {a = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.1520611888-.9119148087e-1*I <- {a = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>34.87574808+12.92049251*I <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>.7143741874e-1+.1030661023*I <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || -  
+
| [https://dlmf.nist.gov/8.8.E1 8.8.E1] || [[Item:Q2533|<math>\incgamma@{a+1}{z} = a\incgamma@{a}{z}-z^{a}e^{-z}</math>]] || <code>GAMMA(a + 1)-GAMMA(a + 1, z)= a*GAMMA(a)-GAMMA(a, z)- (z)^(a)* exp(- z)</code> || <code>Gamma[a + 1, 0, z]= a*Gamma[a, 0, z]- (z)^(a)* Exp[- z]</code> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.135004907e-1-.2375774782*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>.8693672828+.710002389*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>107.1902160-63.3824277*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-.1657436948-.7422690683*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || -  
 
|-
 
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| [https://dlmf.nist.gov/8.8.E2 8.8.E2] || [[Item:Q2534|<math>\incGamma@{a+1}{z} = a\incGamma@{a}{z}+z^{a}e^{-z}</math>]] || <code>GAMMA(a + 1, z)= a*GAMMA(a, z)+ (z)^(a)* exp(- z)</code> || <code>Gamma[a + 1, z]= a*Gamma[a, z]+ (z)^(a)* Exp[- z]</code> || Failure || Successful || Successful || -  
 
| [https://dlmf.nist.gov/8.8.E2 8.8.E2] || [[Item:Q2534|<math>\incGamma@{a+1}{z} = a\incGamma@{a}{z}+z^{a}e^{-z}</math>]] || <code>GAMMA(a + 1, z)= a*GAMMA(a, z)+ (z)^(a)* exp(- z)</code> || <code>Gamma[a + 1, z]= a*Gamma[a, z]+ (z)^(a)* Exp[- z]</code> || Failure || Successful || Successful || -  
Line 151: Line 151:
 
| [https://dlmf.nist.gov/8.8.E16 8.8.E16] || [[Item:Q2548|<math>\deriv[n]{}{z}(z^{-a}\incGamma@{a}{z}) = (-1)^{n}z^{-a-n}\incGamma@{a+n}{z}</math>]] || <code>diff((z)^(- a)* GAMMA(a, z), [z$(n)])=(- 1)^(n)* (z)^(- a - n)* GAMMA(a + n, z)</code> || <code>D[(z)^(- a)* Gamma[a, z], {z, n}]=(- 1)^(n)* (z)^(- a - n)* Gamma[a + n, z]</code> || Failure || Failure || Skip || Skip  
 
| [https://dlmf.nist.gov/8.8.E16 8.8.E16] || [[Item:Q2548|<math>\deriv[n]{}{z}(z^{-a}\incGamma@{a}{z}) = (-1)^{n}z^{-a-n}\incGamma@{a+n}{z}</math>]] || <code>diff((z)^(- a)* GAMMA(a, z), [z$(n)])=(- 1)^(n)* (z)^(- a - n)* GAMMA(a + n, z)</code> || <code>D[(z)^(- a)* Gamma[a, z], {z, n}]=(- 1)^(n)* (z)^(- a - n)* Gamma[a + n, z]</code> || Failure || Failure || Skip || Skip  
 
|-
 
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| [https://dlmf.nist.gov/8.8.E17 8.8.E17] || [[Item:Q2549|<math>\deriv[n]{}{z}(e^{z}\incgamma@{a}{z}) = (-1)^{n}\Pochhammersym{1-a}{n}e^{z}\incgamma@{a-n}{z}</math>]] || <code>diff(exp(z)*GAMMA(a)-GAMMA(a, z), [z$(n)])=(- 1)^(n)* pochhammer(1 - a, n)*exp(z)*GAMMA(a - n)-GAMMA(a - n, z)</code> || <code>D[Exp[z]*Gamma[a, 0, z], {z, n}]=(- 1)^(n)* Pochhammer[1 - a, n]*Exp[z]*Gamma[a - n, 0, z]</code> || Failure || Failure || Skip || Skip
+
| [https://dlmf.nist.gov/8.8.E17 8.8.E17] || [[Item:Q2549|<math>\deriv[n]{}{z}(e^{z}\incgamma@{a}{z}) = (-1)^{n}\Pochhammersym{1-a}{n}e^{z}\incgamma@{a-n}{z}</math>]] || <code>diff(exp(z)*GAMMA(a)-GAMMA(a, z), [z$(n)])=(- 1)^(n)* pochhammer(1 - a, n)*exp(z)*GAMMA(a - n)-GAMMA(a - n, z)</code> || <code>D[Exp[z]*Gamma[a, 0, z], {z, n}]=(- 1)^(n)* Pochhammer[1 - a, n]*Exp[z]*Gamma[a - n, 0, z]</code> || Failure || Failure || Skip || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.8.E18 8.8.E18] || [[Item:Q2550|<math>\deriv[n]{}{z}(z^{a}e^{z}\scincgamma@{a}{z}) = z^{a-n}e^{z}\scincgamma@{a-n}{z}</math>]] || <code>diff((z)^(a)* exp(z)*(z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a), [z$(n)])= (z)^(a - n)* exp(z)*(z)^(-(a - n))*(GAMMA(a - n)-GAMMA(a - n, z))/GAMMA(a - n)</code> || <code>Error</code> || Failure || Error || Skip || -  
 
| [https://dlmf.nist.gov/8.8.E18 8.8.E18] || [[Item:Q2550|<math>\deriv[n]{}{z}(z^{a}e^{z}\scincgamma@{a}{z}) = z^{a-n}e^{z}\scincgamma@{a-n}{z}</math>]] || <code>diff((z)^(a)* exp(z)*(z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a), [z$(n)])= (z)^(a - n)* exp(z)*(z)^(-(a - n))*(GAMMA(a - n)-GAMMA(a - n, z))/GAMMA(a - n)</code> || <code>Error</code> || Failure || Error || Skip || -  
Line 161: Line 161:
 
| [https://dlmf.nist.gov/8.10.E2 8.10.E2] || [[Item:Q2555|<math>\incgamma@{a}{x} >= \frac{x^{a-1}}{a}(1-e^{-x})</math>]] || <code>GAMMA(a)-GAMMA(a, x)> =((x)^(a - 1))/(a)*(1 - exp(- x))</code> || <code>Gamma[a, 0, x]> =Divide[(x)^(a - 1),a]*(1 - Exp[- x])</code> || Failure || Failure || Skip || Successful  
 
| [https://dlmf.nist.gov/8.10.E2 8.10.E2] || [[Item:Q2555|<math>\incgamma@{a}{x} >= \frac{x^{a-1}}{a}(1-e^{-x})</math>]] || <code>GAMMA(a)-GAMMA(a, x)> =((x)^(a - 1))/(a)*(1 - exp(- x))</code> || <code>Gamma[a, 0, x]> =Divide[(x)^(a - 1),a]*(1 - Exp[- x])</code> || Failure || Failure || Skip || Successful  
 
|-
 
|-
| [https://dlmf.nist.gov/8.10.E3 8.10.E3] || [[Item:Q2556|<math>x^{1-a}e^{x}\incGamma@{a}{x} = 1+\frac{a-1}{x}\vartheta</math>]] || <code>(x)^(1 - a)* exp(x)*GAMMA(a, x)= 1 +(a - 1)/(x)*vartheta</code> || <code>(x)^(1 - a)* Exp[x]*Gamma[a, x]= 1 +Divide[a - 1,x]*\[CurlyTheta]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.052938223-1.733408016*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>.6195824495-.7346525318*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.4531580595-.4544327802*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.947061775-.5618351419*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.380417550-.1488660948*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.8801752730-.639084889e-1*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.775488901+3.438164856*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-.7946311125+1.851133904*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.4896509817+1.269424844*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>2.224511097+2.266591982*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>1.205368886+1.265347467*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.8436823508+.8789005523*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.947061775+.5618351419*I <- {a = 2^(1/2)-I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.380417550+.1488660948*I <- {a = 2^(1/2)-I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.8801752730+.639084889e-1*I <- {a = 2^(1/2)-I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>1.052938223+1.733408016*I <- {a = 2^(1/2)-I*2^(1/2), vartheta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>.6195824495+.7346525318*I <- {a = 2^(1/2)-I*2^(1/2), vartheta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>.4531580595+.4544327802*I <- {a = 2^(1/2)-I*2^(1/2), vartheta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>2.224511097-2.266591982*I <- {a = 2^(1/2)-I*2^(1/2), vartheta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>1.205368886-1.265347467*I <- {a = 2^(1/2)-I*2^(1/2), vartheta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>.8436823508-.8789005523*I <- {a = 2^(1/2)-I*2^(1/2), vartheta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.775488901-3.438164856*I <- {a = 2^(1/2)-I*2^(1/2), vartheta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-.7946311125-1.851133904*I <- {a = 2^(1/2)-I*2^(1/2), vartheta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.4896509817-1.269424844*I <- {a = 2^(1/2)-I*2^(1/2), vartheta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>.7137479990+5.279470749*I <- {a = -2^(1/2)-I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>.1689182623+2.559481797*I <- {a = -2^(1/2)-I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.333014351e-1+1.662585688*I <- {a = -2^(1/2)-I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>4.713747997-1.548956373*I <- {a = -2^(1/2)-I*2^(1/2), vartheta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>2.168918261-.8547317639*I <- {a = -2^(1/2)-I*2^(1/2), vartheta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>1.366634768-.6135566855*I <- {a = -2^(1/2)-I*2^(1/2), vartheta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-2.114679125-5.548956371*I <- {a = -2^(1/2)-I*2^(1/2), vartheta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.245295300-2.854731763*I <- {a = -2^(1/2)-I*2^(1/2), vartheta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.9095076061-1.946890018*I <- {a = -2^(1/2)-I*2^(1/2), vartheta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-6.114679123+1.279470751*I <- {a = -2^(1/2)-I*2^(1/2), vartheta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-3.245295299+.5594817981*I <- {a = -2^(1/2)-I*2^(1/2), vartheta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-2.242840938+.3292523557*I <- {a = -2^(1/2)-I*2^(1/2), vartheta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>4.713747997+1.548956373*I <- {a = -2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>2.168918261+.8547317639*I <- {a = -2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>1.366634768+.6135566855*I <- {a = -2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>.7137479990-5.279470749*I <- {a = -2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>.1689182623-2.559481797*I <- {a = -2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>.333014351e-1-1.662585688*I <- {a = -2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-6.114679123-1.279470751*I <- {a = -2^(1/2)+I*2^(1/2), vartheta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-3.245295299-.5594817981*I <- {a = -2^(1/2)+I*2^(1/2), vartheta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-2.242840938-.3292523557*I <- {a = -2^(1/2)+I*2^(1/2), vartheta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-2.114679125+5.548956371*I <- {a = -2^(1/2)+I*2^(1/2), vartheta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.245295300+2.854731763*I <- {a = -2^(1/2)+I*2^(1/2), vartheta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.9095076061+1.946890018*I <- {a = -2^(1/2)+I*2^(1/2), vartheta = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.0529382235611282, -1.733408017034722] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6195824493248067, -0.7346525326366091] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.4531580595377106, -0.4544327806624232] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.947061776438873, -0.5618351417809119] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.3804175506751934, -0.14886609500970405] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8801752737956228, -0.06390848891115308] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.7754889011850625, 3.438164858219089] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.7946311130482883, 1.851133904990296] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.48965098204435287, 1.2694248444221805] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.224511098814938, 2.266591982965279] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.2053688869517116, 1.2653474673633909] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8436823512889807, 0.8789005526709103] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.947061776438873, 0.5618351417809119] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.3804175506751934, 0.14886609500970405] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8801752737956228, 0.06390848891115308] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0529382235611282, 1.733408017034722] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6195824493248067, 0.7346525326366091] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.4531580595377106, 0.4544327806624232] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.224511098814938, -2.266591982965279] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.2053688869517116, -1.2653474673633909] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8436823512889807, -0.8789005526709103] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.7754889011850625, -3.438164858219089] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.7946311130482883, -1.851133904990296] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.48965098204435287, -1.2694248444221805] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7137479994437111, 5.2794707516485415] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.16891826235482466, 2.5594817982620857] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.03330143512454342, 1.6625856892027477] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.713747999443712, -1.5489563730976488] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.1689182623548247, -0.8547317641110086] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3666347684578768, -0.6135566857126489] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.114679125302478, -5.54895637309765] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.2452953000182698, -2.8547317641110084] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.9095076064575197, -1.9468900190459824] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.114679125302479, 1.2794707516485402] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.2452953000182694, 0.5594817982620859] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.2428409397908533, 0.32925235586941426] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.713747999443712, 1.5489563730976488] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.1689182623548247, 0.8547317641110086] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3666347684578768, 0.6135566857126489] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7137479994437111, -5.2794707516485415] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.16891826235482466, -2.5594817982620857] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.03330143512454342, -1.6625856892027477] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.114679125302479, -1.2794707516485402] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.2452953000182694, -0.5594817982620859] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.2428409397908533, -0.32925235586941426] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.114679125302478, 5.54895637309765] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.2452953000182698, 2.8547317641110084] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.9095076064575197, 1.9468900190459824] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/8.10.E3 8.10.E3] || [[Item:Q2556|<math>x^{1-a}e^{x}\incGamma@{a}{x} = 1+\frac{a-1}{x}\vartheta</math>]] || <code>(x)^(1 - a)* exp(x)*GAMMA(a, x)= 1 +(a - 1)/(x)*vartheta</code> || <code>(x)^(1 - a)* Exp[x]*Gamma[a, x]= 1 +Divide[a - 1,x]*\[CurlyTheta]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.052938223-1.733408016*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>.6195824495-.7346525318*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.4531580595-.4544327802*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.947061775-.5618351419*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)-I*2^(1/2), x = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.0529382235611282, -1.733408017034722] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6195824493248067, -0.7346525326366091] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.4531580595377106, -0.4544327806624232] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.947061776438873, -0.5618351417809119] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.10.E5 8.10.E5] || [[Item:Q2558|<math>A_{n} < x^{1-a}e^{x}\incGamma@{a}{x}</math>]] || <code>A[n]< (x)^(1 - a)* exp(x)*GAMMA(a, x)</code> || <code>Subscript[A, n]< (x)^(1 - a)* Exp[x]*Gamma[a, x]</code> || Failure || Failure || Successful || Successful  
 
| [https://dlmf.nist.gov/8.10.E5 8.10.E5] || [[Item:Q2558|<math>A_{n} < x^{1-a}e^{x}\incGamma@{a}{x}</math>]] || <code>A[n]< (x)^(1 - a)* exp(x)*GAMMA(a, x)</code> || <code>Subscript[A, n]< (x)^(1 - a)* Exp[x]*Gamma[a, x]</code> || Failure || Failure || Successful || Successful  
Line 167: Line 167:
 
| [https://dlmf.nist.gov/8.10.E5 8.10.E5] || [[Item:Q2558|<math>x^{1-a}e^{x}\incGamma@{a}{x} < B_{n}</math>]] || <code>(x)^(1 - a)* exp(x)*GAMMA(a, x)< B[n]</code> || <code>(x)^(1 - a)* Exp[x]*Gamma[a, x]< Subscript[B, n]</code> || Failure || Failure || Successful || Successful  
 
| [https://dlmf.nist.gov/8.10.E5 8.10.E5] || [[Item:Q2558|<math>x^{1-a}e^{x}\incGamma@{a}{x} < B_{n}</math>]] || <code>(x)^(1 - a)* exp(x)*GAMMA(a, x)< B[n]</code> || <code>(x)^(1 - a)* Exp[x]*Gamma[a, x]< Subscript[B, n]</code> || Failure || Failure || Successful || Successful  
 
|-
 
|-
| [https://dlmf.nist.gov/8.10.E7 8.10.E7] || [[Item:Q2563|<math>I = \int_{0}^{x}t^{a-1}e^{t}\diff{t}</math>]] || <code>I = int((t)^(a - 1)* exp(t), t = 0..x)</code> || <code>I = Integrate[(t)^(a - 1)* Exp[t], {t, 0, x}]</code> || Failure || Failure || Skip || Skip
+
| [https://dlmf.nist.gov/8.10.E7 8.10.E7] || [[Item:Q2563|<math>I = \int_{0}^{x}t^{a-1}e^{t}\diff{t}</math>]] || <code>I = int((t)^(a - 1)* exp(t), t = 0..x)</code> || <code>I = Integrate[(t)^(a - 1)* Exp[t], {t, 0, x}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-2.925303491814363, 1.0] <- {Rule[a, Rational[1, 2]], Rule[x, 1]}</code><br><code>Complex[-6.687685525621974, 1.0000000000000002] <- {Rule[a, Rational[1, 2]], Rule[x, 2]}</code><br><code>Complex[-14.626171384019093, 1.0000000000000007] <- {Rule[a, Rational[1, 2]], Rule[x, 3]}</code><br></div></div>
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.10.E7 8.10.E7] || [[Item:Q2563|<math>\int_{0}^{x}t^{a-1}e^{t}\diff{t} = \EulerGamma@{a}x^{a}\scincgamma@{a}{-x}</math>]] || <code>int((t)^(a - 1)* exp(t), t = 0..x)= GAMMA(a)*(x)^(a)* (- x)^(-(a))*(GAMMA(a)-GAMMA(a, - x))/GAMMA(a)</code> || <code>Error</code> || Failure || Error || Skip || -  
 
| [https://dlmf.nist.gov/8.10.E7 8.10.E7] || [[Item:Q2563|<math>\int_{0}^{x}t^{a-1}e^{t}\diff{t} = \EulerGamma@{a}x^{a}\scincgamma@{a}{-x}</math>]] || <code>int((t)^(a - 1)* exp(t), t = 0..x)= GAMMA(a)*(x)^(a)* (- x)^(-(a))*(GAMMA(a)-GAMMA(a, - x))/GAMMA(a)</code> || <code>Error</code> || Failure || Error || Skip || -  
 
|-
 
|-
| [https://dlmf.nist.gov/8.10#Ex5 8.10#Ex5] || [[Item:Q2565|<math>c_{a} = (\EulerGamma@{1+a})^{1/(a-1)}</math>]] || <code>c[a]=(GAMMA(1 + a))^(1/(a - 1))</code> || <code>Subscript[c, a]=(Gamma[1 + a])^(1/(a - 1))</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.342222950+.7512982152*I <- {a = 2^(1/2)+I*2^(1/2), c[a] = 2^(1/2)+I*2^(1/2)}</code><br><code>-.342222950-2.077128909*I <- {a = 2^(1/2)+I*2^(1/2), c[a] = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.170650074-2.077128909*I <- {a = 2^(1/2)+I*2^(1/2), c[a] = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.170650074+.7512982152*I <- {a = 2^(1/2)+I*2^(1/2), c[a] = -2^(1/2)+I*2^(1/2)}</code><br><code>-.342222950+2.077128909*I <- {a = 2^(1/2)-I*2^(1/2), c[a] = 2^(1/2)+I*2^(1/2)}</code><br><code>-.342222950-.7512982152*I <- {a = 2^(1/2)-I*2^(1/2), c[a] = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.170650074-.7512982152*I <- {a = 2^(1/2)-I*2^(1/2), c[a] = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.170650074+2.077128909*I <- {a = 2^(1/2)-I*2^(1/2), c[a] = -2^(1/2)+I*2^(1/2)}</code><br><code>.9491134946+2.345189180*I <- {a = -2^(1/2)-I*2^(1/2), c[a] = 2^(1/2)+I*2^(1/2)}</code><br><code>.9491134946-.4832379435*I <- {a = -2^(1/2)-I*2^(1/2), c[a] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.879313629-.4832379435*I <- {a = -2^(1/2)-I*2^(1/2), c[a] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.879313629+2.345189180*I <- {a = -2^(1/2)-I*2^(1/2), c[a] = -2^(1/2)+I*2^(1/2)}</code><br><code>.9491134946+.4832379435*I <- {a = -2^(1/2)+I*2^(1/2), c[a] = 2^(1/2)+I*2^(1/2)}</code><br><code>.9491134946-2.345189180*I <- {a = -2^(1/2)+I*2^(1/2), c[a] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.879313629-2.345189180*I <- {a = -2^(1/2)+I*2^(1/2), c[a] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.879313629+.4832379435*I <- {a = -2^(1/2)+I*2^(1/2), c[a] = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || Successful  
+
| [https://dlmf.nist.gov/8.10#Ex5 8.10#Ex5] || [[Item:Q2565|<math>c_{a} = (\EulerGamma@{1+a})^{1/(a-1)}</math>]] || <code>c[a]=(GAMMA(1 + a))^(1/(a - 1))</code> || <code>Subscript[c, a]=(Gamma[1 + a])^(1/(a - 1))</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.342222950+.7512982152*I <- {a = 2^(1/2)+I*2^(1/2), c[a] = 2^(1/2)+I*2^(1/2)}</code><br><code>-.342222950-2.077128909*I <- {a = 2^(1/2)+I*2^(1/2), c[a] = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.170650074-2.077128909*I <- {a = 2^(1/2)+I*2^(1/2), c[a] = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.170650074+.7512982152*I <- {a = 2^(1/2)+I*2^(1/2), c[a] = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Successful  
 
|-
 
|-
| [https://dlmf.nist.gov/8.10#Ex6 8.10#Ex6] || [[Item:Q2566|<math>d_{a} = (\EulerGamma@{1+a})^{-1/a}</math>]] || <code>d[a]=(GAMMA(1 + a))^(- 1/ a)</code> || <code>Subscript[d, a]=(Gamma[1 + a])^(- 1/ a)</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.7353701374+1.747162536*I <- {a = 2^(1/2)+I*2^(1/2), d[a] = 2^(1/2)+I*2^(1/2)}</code><br><code>.7353701374-1.081264588*I <- {a = 2^(1/2)+I*2^(1/2), d[a] = 2^(1/2)-I*2^(1/2)}</code><br><code>-2.093056987-1.081264588*I <- {a = 2^(1/2)+I*2^(1/2), d[a] = -2^(1/2)-I*2^(1/2)}</code><br><code>-2.093056987+1.747162536*I <- {a = 2^(1/2)+I*2^(1/2), d[a] = -2^(1/2)+I*2^(1/2)}</code><br><code>.7353701374+1.081264588*I <- {a = 2^(1/2)-I*2^(1/2), d[a] = 2^(1/2)+I*2^(1/2)}</code><br><code>.7353701374-1.747162536*I <- {a = 2^(1/2)-I*2^(1/2), d[a] = 2^(1/2)-I*2^(1/2)}</code><br><code>-2.093056987-1.747162536*I <- {a = 2^(1/2)-I*2^(1/2), d[a] = -2^(1/2)-I*2^(1/2)}</code><br><code>-2.093056987+1.081264588*I <- {a = 2^(1/2)-I*2^(1/2), d[a] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.333446246+.15004730e-1*I <- {a = -2^(1/2)-I*2^(1/2), d[a] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.333446246-2.813422394*I <- {a = -2^(1/2)-I*2^(1/2), d[a] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.494980878-2.813422394*I <- {a = -2^(1/2)-I*2^(1/2), d[a] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.494980878+.15004730e-1*I <- {a = -2^(1/2)-I*2^(1/2), d[a] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.333446246+2.813422394*I <- {a = -2^(1/2)+I*2^(1/2), d[a] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.333446246-.15004730e-1*I <- {a = -2^(1/2)+I*2^(1/2), d[a] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.494980878-.15004730e-1*I <- {a = -2^(1/2)+I*2^(1/2), d[a] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.494980878+2.813422394*I <- {a = -2^(1/2)+I*2^(1/2), d[a] = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || Successful  
+
| [https://dlmf.nist.gov/8.10#Ex6 8.10#Ex6] || [[Item:Q2566|<math>d_{a} = (\EulerGamma@{1+a})^{-1/a}</math>]] || <code>d[a]=(GAMMA(1 + a))^(- 1/ a)</code> || <code>Subscript[d, a]=(Gamma[1 + a])^(- 1/ a)</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.7353701374+1.747162536*I <- {a = 2^(1/2)+I*2^(1/2), d[a] = 2^(1/2)+I*2^(1/2)}</code><br><code>.7353701374-1.081264588*I <- {a = 2^(1/2)+I*2^(1/2), d[a] = 2^(1/2)-I*2^(1/2)}</code><br><code>-2.093056987-1.081264588*I <- {a = 2^(1/2)+I*2^(1/2), d[a] = -2^(1/2)-I*2^(1/2)}</code><br><code>-2.093056987+1.747162536*I <- {a = 2^(1/2)+I*2^(1/2), d[a] = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Successful  
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.10.E10 8.10.E10] || [[Item:Q2567|<math>\frac{x}{2a}\left(\left(1+\frac{2}{x}\right)^{a}-1\right) < x^{1-a}e^{x}\incGamma@{a}{x}</math>]] || <code>(x)/(2*a)*((1 +(2)/(x))^(a)- 1)< (x)^(1 - a)* exp(x)*GAMMA(a, x)</code> || <code>Divide[x,2*a]*((1 +Divide[2,x])^(a)- 1)< (x)^(1 - a)* Exp[x]*Gamma[a, x]</code> || Failure || Failure || Successful || Successful  
 
| [https://dlmf.nist.gov/8.10.E10 8.10.E10] || [[Item:Q2567|<math>\frac{x}{2a}\left(\left(1+\frac{2}{x}\right)^{a}-1\right) < x^{1-a}e^{x}\incGamma@{a}{x}</math>]] || <code>(x)/(2*a)*((1 +(2)/(x))^(a)- 1)< (x)^(1 - a)* exp(x)*GAMMA(a, x)</code> || <code>Divide[x,2*a]*((1 +Divide[2,x])^(a)- 1)< (x)^(1 - a)* Exp[x]*Gamma[a, x]</code> || Failure || Failure || Successful || Successful  
Line 191: Line 191:
 
| [https://dlmf.nist.gov/8.11.E4 8.11.E4] || [[Item:Q2575|<math>\incgamma@{a}{z} = z^{a}e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\Pochhammersym{a}{k+1}}</math>]] || <code>GAMMA(a)-GAMMA(a, z)= (z)^(a)* exp(- z)*sum(((z)^(k))/(pochhammer(a, k + 1)), k = 0..infinity)</code> || <code>Gamma[a, 0, z]= (z)^(a)* Exp[- z]*Sum[Divide[(z)^(k),Pochhammer[a, k + 1]], {k, 0, Infinity}]</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/8.11.E4 8.11.E4] || [[Item:Q2575|<math>\incgamma@{a}{z} = z^{a}e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\Pochhammersym{a}{k+1}}</math>]] || <code>GAMMA(a)-GAMMA(a, z)= (z)^(a)* exp(- z)*sum(((z)^(k))/(pochhammer(a, k + 1)), k = 0..infinity)</code> || <code>Gamma[a, 0, z]= (z)^(a)* Exp[- z]*Sum[Divide[(z)^(k),Pochhammer[a, k + 1]], {k, 0, Infinity}]</code> || Successful || Successful || - || -  
 
|-
 
|-
| [https://dlmf.nist.gov/8.11.E15 8.11.E15] || [[Item:Q2588|<math>S_{n}(x) = \frac{\incgamma@{n+1}{nx}}{(nx)^{n}e^{-nx}}</math>]] || <code>S[n]*(x)=(GAMMA(n + 1)-GAMMA(n + 1, n*x))/((n*x)^(n)* exp(- n*x))</code> || <code>Subscript[S, n]*(x)=Divide[Gamma[n + 1, 0, n*x],(n*x)^(n)* Exp[- n*x]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.6959317335+1.414213562*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 1, x = 1}</code><br><code>.633899074+2.828427124*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 1, x = 2}</code><br><code>-1.119204955+4.242640686*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 1, x = 3}</code><br><code>.219685512+1.414213562*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 2, x = 1}</code><br><code>-2.371341630+2.828427124*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 2, x = 2}</code><br><code>-16.78118116+4.242640686*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 2, x = 3}</code><br><code>-.160350198+1.414213562*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 3, x = 1}</code><br><code>-6.683483804+2.828427124*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 3, x = 2}</code><br><code>-61.03377023+4.242640686*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 3, x = 3}</code><br><code>.6959317335-1.414213562*I <- {S[n] = 2^(1/2)-I*2^(1/2), n = 1, x = 1}</code><br><code>.633899074-2.828427124*I <- {S[n] = 2^(1/2)-I*2^(1/2), n = 1, x = 2}</code><br><code>-1.119204955-4.242640686*I <- {S[n] = 2^(1/2)-I*2^(1/2), n = 1, x = 3}</code><br><code>.219685512-1.414213562*I <- {S[n] = 2^(1/2)-I*2^(1/2), n = 2, x = 1}</code><br><code>-2.371341630-2.828427124*I <- {S[n] = 2^(1/2)-I*2^(1/2), n = 2, x = 2}</code><br><code>-16.78118116-4.242640686*I <- {S[n] = 2^(1/2)-I*2^(1/2), n = 2, x = 3}</code><br><code>-.160350198-1.414213562*I <- {S[n] = 2^(1/2)-I*2^(1/2), n = 3, x = 1}</code><br><code>-6.683483804-2.828427124*I <- {S[n] = 2^(1/2)-I*2^(1/2), n = 3, x = 2}</code><br><code>-61.03377023-4.242640686*I <- {S[n] = 2^(1/2)-I*2^(1/2), n = 3, x = 3}</code><br><code>-2.132495390-1.414213562*I <- {S[n] = -2^(1/2)-I*2^(1/2), n = 1, x = 1}</code><br><code>-5.022955174-2.828427124*I <- {S[n] = -2^(1/2)-I*2^(1/2), n = 1, x = 2}</code><br><code>-9.604486327-4.242640686*I <- {S[n] = -2^(1/2)-I*2^(1/2), n = 1, x = 3}</code><br><code>-2.608741612-1.414213562*I <- {S[n] = -2^(1/2)-I*2^(1/2), n = 2, x = 1}</code><br><code>-8.028195878-2.828427124*I <- {S[n] = -2^(1/2)-I*2^(1/2), n = 2, x = 2}</code><br><code>-25.26646254-4.242640686*I <- {S[n] = -2^(1/2)-I*2^(1/2), n = 2, x = 3}</code><br><code>-2.988777322-1.414213562*I <- {S[n] = -2^(1/2)-I*2^(1/2), n = 3, x = 1}</code><br><code>-12.34033805-2.828427124*I <- {S[n] = -2^(1/2)-I*2^(1/2), n = 3, x = 2}</code><br><code>-69.51905161-4.242640686*I <- {S[n] = -2^(1/2)-I*2^(1/2), n = 3, x = 3}</code><br><code>-2.132495390+1.414213562*I <- {S[n] = -2^(1/2)+I*2^(1/2), n = 1, x = 1}</code><br><code>-5.022955174+2.828427124*I <- {S[n] = -2^(1/2)+I*2^(1/2), n = 1, x = 2}</code><br><code>-9.604486327+4.242640686*I <- {S[n] = -2^(1/2)+I*2^(1/2), n = 1, x = 3}</code><br><code>-2.608741612+1.414213562*I <- {S[n] = -2^(1/2)+I*2^(1/2), n = 2, x = 1}</code><br><code>-8.028195878+2.828427124*I <- {S[n] = -2^(1/2)+I*2^(1/2), n = 2, x = 2}</code><br><code>-25.26646254+4.242640686*I <- {S[n] = -2^(1/2)+I*2^(1/2), n = 2, x = 3}</code><br><code>-2.988777322+1.414213562*I <- {S[n] = -2^(1/2)+I*2^(1/2), n = 3, x = 1}</code><br><code>-12.34033805+2.828427124*I <- {S[n] = -2^(1/2)+I*2^(1/2), n = 3, x = 2}</code><br><code>-69.51905161+4.242640686*I <- {S[n] = -2^(1/2)+I*2^(1/2), n = 3, x = 3}</code><br></div></div> || Successful  
+
| [https://dlmf.nist.gov/8.11.E15 8.11.E15] || [[Item:Q2588|<math>S_{n}(x) = \frac{\incgamma@{n+1}{nx}}{(nx)^{n}e^{-nx}}</math>]] || <code>S[n]*(x)=(GAMMA(n + 1)-GAMMA(n + 1, n*x))/((n*x)^(n)* exp(- n*x))</code> || <code>Subscript[S, n]*(x)=Divide[Gamma[n + 1, 0, n*x],(n*x)^(n)* Exp[- n*x]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.6959317335+1.414213562*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 1, x = 1}</code><br><code>.633899074+2.828427124*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 1, x = 2}</code><br><code>-1.119204955+4.242640686*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 1, x = 3}</code><br><code>.219685512+1.414213562*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 2, x = 1}</code><br>... skip entries to safe data<br></div></div> || Successful  
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.12.E3 8.12.E3] || [[Item:Q2597|<math>\normincGammaP@{a}{z} = \tfrac{1}{2}\erfc@{-\eta\sqrt{a/2}}-S(a,\eta)</math>]] || <code>(GAMMA(a)-GAMMA(a, z))/GAMMA(a)=(1)/(2)*erfc(- eta*sqrt(a/ 2))- S*(a , eta)</code> || <code>GammaRegularized[a, 0, z]=Divide[1,2]*Erfc[- \[Eta]*Sqrt[a/ 2]]- S*(a , \[Eta])</code> || Failure || Failure || Error || Error  
 
| [https://dlmf.nist.gov/8.12.E3 8.12.E3] || [[Item:Q2597|<math>\normincGammaP@{a}{z} = \tfrac{1}{2}\erfc@{-\eta\sqrt{a/2}}-S(a,\eta)</math>]] || <code>(GAMMA(a)-GAMMA(a, z))/GAMMA(a)=(1)/(2)*erfc(- eta*sqrt(a/ 2))- S*(a , eta)</code> || <code>GammaRegularized[a, 0, z]=Divide[1,2]*Erfc[- \[Eta]*Sqrt[a/ 2]]- S*(a , \[Eta])</code> || Failure || Failure || Error || Error  
Line 209: Line 209:
 
| [https://dlmf.nist.gov/8.12.E10 8.12.E10] || [[Item:Q2606|<math>c_{k}(\eta) = \frac{1}{\eta}\deriv{}{\eta}c_{k-1}(\eta)+(-1)^{k}\frac{g_{k}}{\mu}</math>]] || <code>c[k]*(eta)=(1)/(eta)*diff(c[k - 1]*(eta), eta)+(- 1)^(k)*(g[k])/(mu)</code> || <code>Subscript[c, k]*(\[Eta])=Divide[1,\[Eta]]*D[Subscript[c, k - 1]*(\[Eta]), \[Eta]]+(- 1)^(k)*Divide[Subscript[g, k],\[Mu]]</code> || Failure || Failure || Skip || Skip  
 
| [https://dlmf.nist.gov/8.12.E10 8.12.E10] || [[Item:Q2606|<math>c_{k}(\eta) = \frac{1}{\eta}\deriv{}{\eta}c_{k-1}(\eta)+(-1)^{k}\frac{g_{k}}{\mu}</math>]] || <code>c[k]*(eta)=(1)/(eta)*diff(c[k - 1]*(eta), eta)+(- 1)^(k)*(g[k])/(mu)</code> || <code>Subscript[c, k]*(\[Eta])=Divide[1,\[Eta]]*D[Subscript[c, k - 1]*(\[Eta]), \[Eta]]+(- 1)^(k)*Divide[Subscript[g, k],\[Mu]]</code> || Failure || Failure || Skip || Skip  
 
|-
 
|-
| [https://dlmf.nist.gov/8.12#Ex23 8.12#Ex23] || [[Item:Q2627|<math>d(+\chi) = \sqrt{\tfrac{1}{2}\pi}e^{\chi^{2}/2}\erfc@{+\chi/\sqrt{2}}</math>]] || <code>d*(+ chi)=sqrt((1)/(2)*Pi)*exp((chi)^(2)/ 2)*erfc(+ chi/sqrt(2))</code> || <code>d*(+ \[Chi])=Sqrt[Divide[1,2]*Pi]*Exp[(\[Chi])^(2)/ 2]*Erfc[+ \[Chi]/Sqrt[2]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.3819402210+4.260963736*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)+I*2^(1/2)}</code><br><code>3.618059777+.2609637385*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)-I*2^(1/2)}</code><br><code>-.3819402210-3.739036260*I <- {chi = 2^(1/2)+I*2^(1/2), d = -2^(1/2)-I*2^(1/2)}</code><br><code>-4.381940219+.2609637385*I <- {chi = 2^(1/2)+I*2^(1/2), d = -2^(1/2)+I*2^(1/2)}</code><br><code>3.618059777-.2609637385*I <- {chi = 2^(1/2)-I*2^(1/2), d = 2^(1/2)+I*2^(1/2)}</code><br><code>-.3819402210-4.260963736*I <- {chi = 2^(1/2)-I*2^(1/2), d = 2^(1/2)-I*2^(1/2)}</code><br><code>-4.381940219-.2609637385*I <- {chi = 2^(1/2)-I*2^(1/2), d = -2^(1/2)-I*2^(1/2)}</code><br><code>-.3819402210+3.739036260*I <- {chi = 2^(1/2)-I*2^(1/2), d = -2^(1/2)+I*2^(1/2)}</code><br><code>1.425065646-6.540234377*I <- {chi = -2^(1/2)-I*2^(1/2), d = 2^(1/2)+I*2^(1/2)}</code><br><code>-2.574934352-2.540234379*I <- {chi = -2^(1/2)-I*2^(1/2), d = 2^(1/2)-I*2^(1/2)}</code><br><code>1.425065646+1.459765619*I <- {chi = -2^(1/2)-I*2^(1/2), d = -2^(1/2)-I*2^(1/2)}</code><br><code>5.425065644-2.540234379*I <- {chi = -2^(1/2)-I*2^(1/2), d = -2^(1/2)+I*2^(1/2)}</code><br><code>-2.574934352+2.540234379*I <- {chi = -2^(1/2)+I*2^(1/2), d = 2^(1/2)+I*2^(1/2)}</code><br><code>1.425065646+6.540234377*I <- {chi = -2^(1/2)+I*2^(1/2), d = 2^(1/2)-I*2^(1/2)}</code><br><code>5.425065644+2.540234379*I <- {chi = -2^(1/2)+I*2^(1/2), d = -2^(1/2)-I*2^(1/2)}</code><br><code>1.425065646-1.459765619*I <- {chi = -2^(1/2)+I*2^(1/2), d = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.3819402207134648, 4.260963738906431] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6180597792865354, -0.26096373890643143] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.425065647600777, -6.540234379036898] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.574934352399223, 2.5402343790368977] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6180597792865354, 0.26096373890643143] <- {Rule[d, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3819402207134648, -4.260963738906431] <- {Rule[d, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.574934352399223, -2.5402343790368977] <- {Rule[d, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.425065647600777, 6.540234379036898] <- {Rule[d, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3819402207134648, -3.7390362610935686] <- {Rule[d, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.381940220713465, -0.26096373890643143] <- {Rule[d, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.425065647600777, 1.4597656209631023] <- {Rule[d, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.425065647600777, 2.5402343790368977] <- {Rule[d, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.381940220713465, 0.26096373890643143] <- {Rule[d, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3819402207134648, 3.7390362610935686] <- {Rule[d, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.425065647600777, -2.5402343790368977] <- {Rule[d, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.425065647600777, -1.4597656209631023] <- {Rule[d, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/8.12#Ex23 8.12#Ex23] || [[Item:Q2627|<math>d(+\chi) = \sqrt{\tfrac{1}{2}\pi}e^{\chi^{2}/2}\erfc@{+\chi/\sqrt{2}}</math>]] || <code>d*(+ chi)=sqrt((1)/(2)*Pi)*exp((chi)^(2)/ 2)*erfc(+ chi/sqrt(2))</code> || <code>d*(+ \[Chi])=Sqrt[Divide[1,2]*Pi]*Exp[(\[Chi])^(2)/ 2]*Erfc[+ \[Chi]/Sqrt[2]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.3819402210+4.260963736*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)+I*2^(1/2)}</code><br><code>3.618059777+.2609637385*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)-I*2^(1/2)}</code><br><code>-.3819402210-3.739036260*I <- {chi = 2^(1/2)+I*2^(1/2), d = -2^(1/2)-I*2^(1/2)}</code><br><code>-4.381940219+.2609637385*I <- {chi = 2^(1/2)+I*2^(1/2), d = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.3819402207134648, 4.260963738906431] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6180597792865354, -0.26096373890643143] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.425065647600777, -6.540234379036898] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.574934352399223, 2.5402343790368977] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
| [https://dlmf.nist.gov/8.12#Ex23 8.12#Ex23] || [[Item:Q2627|<math>d(-\chi) = \sqrt{\tfrac{1}{2}\pi}e^{\chi^{2}/2}\erfc@{-\chi/\sqrt{2}}</math>]] || <code>d*(- chi)=sqrt((1)/(2)*Pi)*exp((chi)^(2)/ 2)*erfc(- chi/sqrt(2))</code> || <code>d*(- \[Chi])=Sqrt[Divide[1,2]*Pi]*Exp[(\[Chi])^(2)/ 2]*Erfc[- \[Chi]/Sqrt[2]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.425065646-6.540234377*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)+I*2^(1/2)}</code><br><code>-2.574934352-2.540234379*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)-I*2^(1/2)}</code><br><code>1.425065646+1.459765619*I <- {chi = 2^(1/2)+I*2^(1/2), d = -2^(1/2)-I*2^(1/2)}</code><br><code>5.425065644-2.540234379*I <- {chi = 2^(1/2)+I*2^(1/2), d = -2^(1/2)+I*2^(1/2)}</code><br><code>-2.574934352+2.540234379*I <- {chi = 2^(1/2)-I*2^(1/2), d = 2^(1/2)+I*2^(1/2)}</code><br><code>1.425065646+6.540234377*I <- {chi = 2^(1/2)-I*2^(1/2), d = 2^(1/2)-I*2^(1/2)}</code><br><code>5.425065644+2.540234379*I <- {chi = 2^(1/2)-I*2^(1/2), d = -2^(1/2)-I*2^(1/2)}</code><br><code>1.425065646-1.459765619*I <- {chi = 2^(1/2)-I*2^(1/2), d = -2^(1/2)+I*2^(1/2)}</code><br><code>-.3819402210+4.260963736*I <- {chi = -2^(1/2)-I*2^(1/2), d = 2^(1/2)+I*2^(1/2)}</code><br><code>3.618059777+.2609637385*I <- {chi = -2^(1/2)-I*2^(1/2), d = 2^(1/2)-I*2^(1/2)}</code><br><code>-.3819402210-3.739036260*I <- {chi = -2^(1/2)-I*2^(1/2), d = -2^(1/2)-I*2^(1/2)}</code><br><code>-4.381940219+.2609637385*I <- {chi = -2^(1/2)-I*2^(1/2), d = -2^(1/2)+I*2^(1/2)}</code><br><code>3.618059777-.2609637385*I <- {chi = -2^(1/2)+I*2^(1/2), d = 2^(1/2)+I*2^(1/2)}</code><br><code>-.3819402210-4.260963736*I <- {chi = -2^(1/2)+I*2^(1/2), d = 2^(1/2)-I*2^(1/2)}</code><br><code>-4.381940219-.2609637385*I <- {chi = -2^(1/2)+I*2^(1/2), d = -2^(1/2)-I*2^(1/2)}</code><br><code>-.3819402210+3.739036260*I <- {chi = -2^(1/2)+I*2^(1/2), d = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.425065647600777, -6.540234379036898] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.574934352399223, 2.5402343790368977] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3819402207134648, 4.260963738906431] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6180597792865354, -0.26096373890643143] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.574934352399223, -2.5402343790368977] <- {Rule[d, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.425065647600777, 6.540234379036898] <- {Rule[d, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6180597792865354, 0.26096373890643143] <- {Rule[d, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3819402207134648, -4.260963738906431] <- {Rule[d, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.425065647600777, 1.4597656209631023] <- {Rule[d, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.425065647600777, 2.5402343790368977] <- {Rule[d, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3819402207134648, -3.7390362610935686] <- {Rule[d, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.381940220713465, -0.26096373890643143] <- {Rule[d, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.425065647600777, -2.5402343790368977] <- {Rule[d, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.425065647600777, -1.4597656209631023] <- {Rule[d, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.381940220713465, 0.26096373890643143] <- {Rule[d, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3819402207134648, 3.7390362610935686] <- {Rule[d, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/8.12#Ex23 8.12#Ex23] || [[Item:Q2627|<math>d(-\chi) = \sqrt{\tfrac{1}{2}\pi}e^{\chi^{2}/2}\erfc@{-\chi/\sqrt{2}}</math>]] || <code>d*(- chi)=sqrt((1)/(2)*Pi)*exp((chi)^(2)/ 2)*erfc(- chi/sqrt(2))</code> || <code>d*(- \[Chi])=Sqrt[Divide[1,2]*Pi]*Exp[(\[Chi])^(2)/ 2]*Erfc[- \[Chi]/Sqrt[2]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.425065646-6.540234377*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)+I*2^(1/2)}</code><br><code>-2.574934352-2.540234379*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)-I*2^(1/2)}</code><br><code>1.425065646+1.459765619*I <- {chi = 2^(1/2)+I*2^(1/2), d = -2^(1/2)-I*2^(1/2)}</code><br><code>5.425065644-2.540234379*I <- {chi = 2^(1/2)+I*2^(1/2), d = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.425065647600777, -6.540234379036898] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.574934352399223, 2.5402343790368977] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3819402207134648, 4.260963738906431] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6180597792865354, -0.26096373890643143] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
| [https://dlmf.nist.gov/8.12.E21 8.12.E21] || [[Item:Q2631|<math>\normincGammaQ@{a}{x} = q</math>]] || <code>GAMMA(a, x)/GAMMA(a)= q</code> || <code>GammaRegularized[a, x]= q</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.6276752047-.7874152397*I <- {a = 2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.269609688-.9406490460*I <- {a = 2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-1.440152063-1.201678512*I <- {a = 2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-.6276752047+2.041011884*I <- {a = 2^(1/2)+I*2^(1/2), q = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.269609688+1.887778078*I <- {a = 2^(1/2)+I*2^(1/2), q = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-1.440152063+1.626748612*I <- {a = 2^(1/2)+I*2^(1/2), q = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>2.200751919+2.041011884*I <- {a = 2^(1/2)+I*2^(1/2), q = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>1.558817436+1.887778078*I <- {a = 2^(1/2)+I*2^(1/2), q = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>1.388275061+1.626748612*I <- {a = 2^(1/2)+I*2^(1/2), q = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>2.200751919-.7874152397*I <- {a = 2^(1/2)+I*2^(1/2), q = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>1.558817436-.9406490460*I <- {a = 2^(1/2)+I*2^(1/2), q = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>1.388275061-1.201678512*I <- {a = 2^(1/2)+I*2^(1/2), q = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-.6276752047-2.041011884*I <- {a = 2^(1/2)-I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.269609688-1.887778078*I <- {a = 2^(1/2)-I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-1.440152063-1.626748612*I <- {a = 2^(1/2)-I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-.6276752047+.7874152397*I <- {a = 2^(1/2)-I*2^(1/2), q = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.269609688+.9406490460*I <- {a = 2^(1/2)-I*2^(1/2), q = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-1.440152063+1.201678512*I <- {a = 2^(1/2)-I*2^(1/2), q = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>2.200751919+.7874152397*I <- {a = 2^(1/2)-I*2^(1/2), q = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>1.558817436+.9406490460*I <- {a = 2^(1/2)-I*2^(1/2), q = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>1.388275061+1.201678512*I <- {a = 2^(1/2)-I*2^(1/2), q = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>2.200751919-2.041011884*I <- {a = 2^(1/2)-I*2^(1/2), q = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>1.558817436-1.887778078*I <- {a = 2^(1/2)-I*2^(1/2), q = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>1.388275061-1.626748612*I <- {a = 2^(1/2)-I*2^(1/2), q = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-.6092675686-.4265523839*I <- {a = -2^(1/2)-I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.284432666-1.411612566*I <- {a = -2^(1/2)-I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-1.395305789-1.424341618*I <- {a = -2^(1/2)-I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-.6092675686+2.401874740*I <- {a = -2^(1/2)-I*2^(1/2), q = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.284432666+1.416814558*I <- {a = -2^(1/2)-I*2^(1/2), q = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-1.395305789+1.404085506*I <- {a = -2^(1/2)-I*2^(1/2), q = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>2.219159555+2.401874740*I <- {a = -2^(1/2)-I*2^(1/2), q = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>1.543994458+1.416814558*I <- {a = -2^(1/2)-I*2^(1/2), q = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>1.433121335+1.404085506*I <- {a = -2^(1/2)-I*2^(1/2), q = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>2.219159555-.4265523839*I <- {a = -2^(1/2)-I*2^(1/2), q = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>1.543994458-1.411612566*I <- {a = -2^(1/2)-I*2^(1/2), q = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>1.433121335-1.424341618*I <- {a = -2^(1/2)-I*2^(1/2), q = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-.6092675686-2.401874740*I <- {a = -2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.284432666-1.416814558*I <- {a = -2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-1.395305789-1.404085506*I <- {a = -2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-.6092675686+.4265523839*I <- {a = -2^(1/2)+I*2^(1/2), q = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.284432666+1.411612566*I <- {a = -2^(1/2)+I*2^(1/2), q = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-1.395305789+1.424341618*I <- {a = -2^(1/2)+I*2^(1/2), q = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>2.219159555+.4265523839*I <- {a = -2^(1/2)+I*2^(1/2), q = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>1.543994458+1.411612566*I <- {a = -2^(1/2)+I*2^(1/2), q = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>1.433121335+1.424341618*I <- {a = -2^(1/2)+I*2^(1/2), q = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>2.219159555-2.401874740*I <- {a = -2^(1/2)+I*2^(1/2), q = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>1.543994458-1.416814558*I <- {a = -2^(1/2)+I*2^(1/2), q = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>1.433121335-1.404085506*I <- {a = -2^(1/2)+I*2^(1/2), q = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.6276752046971461, -0.7874152400294763] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[-1.2696096879275383, -0.9406490461902074] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[-1.4401520638257446, -1.2016785120794473] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[-0.6276752046971461, 2.0410118847167142] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[-1.2696096879275383, 1.887778078555983] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[-1.4401520638257446, 1.626748612666743] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[2.2007519200490444, 2.0410118847167142] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[1.558817436818652, 1.887778078555983] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[1.3882750609204457, 1.626748612666743] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[2.2007519200490444, -0.7874152400294763] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[1.558817436818652, -0.9406490461902074] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[1.3882750609204457, -1.2016785120794473] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[-0.6276752046971461, -2.0410118847167142] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[-1.2696096879275383, -1.887778078555983] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[-1.4401520638257446, -1.626748612666743] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[-0.6276752046971461, 0.7874152400294763] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[-1.2696096879275383, 0.9406490461902074] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[-1.4401520638257446, 1.2016785120794473] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[2.2007519200490444, 0.7874152400294763] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[1.558817436818652, 0.9406490461902074] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[1.3882750609204457, 1.2016785120794473] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[2.2007519200490444, -2.0410118847167142] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[1.558817436818652, -1.887778078555983] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[1.3882750609204457, -1.626748612666743] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[-0.6092675673315685, -0.4265523833459248] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[-1.284432666118112, -1.4116125669358923] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[-1.3953057896153958, -1.4243416188305085] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[-0.6092675673315685, 2.4018747414002655] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[-1.284432666118112, 1.416814557810298] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[-1.3953057896153958, 1.4040855059156818] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[2.219159557414622, 2.4018747414002655] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[1.5439944586280783, 1.416814557810298] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[1.4331213351307945, 1.4040855059156818] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[2.219159557414622, -0.4265523833459248] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[1.5439944586280783, -1.4116125669358923] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[1.4331213351307945, -1.4243416188305085] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[-0.6092675673315685, -2.4018747414002655] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[-1.284432666118112, -1.416814557810298] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[-1.3953057896153958, -1.4040855059156818] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[-0.6092675673315685, 0.4265523833459248] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[-1.284432666118112, 1.4116125669358923] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[-1.3953057896153958, 1.4243416188305085] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[2.219159557414622, 0.4265523833459248] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[1.5439944586280783, 1.4116125669358923] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[1.4331213351307945, 1.4243416188305085] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[2.219159557414622, -2.4018747414002655] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[1.5439944586280783, -1.416814557810298] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[1.4331213351307945, -1.4040855059156818] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/8.12.E21 8.12.E21] || [[Item:Q2631|<math>\normincGammaQ@{a}{x} = q</math>]] || <code>GAMMA(a, x)/GAMMA(a)= q</code> || <code>GammaRegularized[a, x]= q</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.6276752047-.7874152397*I <- {a = 2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.269609688-.9406490460*I <- {a = 2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-1.440152063-1.201678512*I <- {a = 2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-.6276752047+2.041011884*I <- {a = 2^(1/2)+I*2^(1/2), q = 2^(1/2)-I*2^(1/2), x = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.6276752046971461, -0.7874152400294763] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[-1.2696096879275383, -0.9406490461902074] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[-1.4401520638257446, -1.2016785120794473] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[-0.6276752046971461, 2.0410118847167142] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.13.E1 8.13.E1] || [[Item:Q2633|<math>1+a^{-1} < x_{-}(a)</math>]] || <code>1 + (a)^(- 1)< x[-]*(a)</code> || <code>1 + (a)^(- 1)< Subscript[x, -]*(a)</code> || Error || Failure || - || Error  
 
| [https://dlmf.nist.gov/8.13.E1 8.13.E1] || [[Item:Q2633|<math>1+a^{-1} < x_{-}(a)</math>]] || <code>1 + (a)^(- 1)< x[-]*(a)</code> || <code>1 + (a)^(- 1)< Subscript[x, -]*(a)</code> || Error || Failure || - || Error  
Line 225: Line 225:
 
| [https://dlmf.nist.gov/8.14.E3 8.14.E3] || [[Item:Q2636|<math>\int_{0}^{\infty}x^{a-1}\incgamma@{b}{x}\diff{x} = -\frac{\EulerGamma@{a+b}}{a}</math>]] || <code>int((x)^(a - 1)* GAMMA(b)-GAMMA(b, x), x = 0..infinity)= -(GAMMA(a + b))/(a)</code> || <code>Integrate[(x)^(a - 1)* Gamma[b, 0, x], {x, 0, Infinity}]= -Divide[Gamma[a + b],a]</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/8.14.E3 8.14.E3] || [[Item:Q2636|<math>\int_{0}^{\infty}x^{a-1}\incgamma@{b}{x}\diff{x} = -\frac{\EulerGamma@{a+b}}{a}</math>]] || <code>int((x)^(a - 1)* GAMMA(b)-GAMMA(b, x), x = 0..infinity)= -(GAMMA(a + b))/(a)</code> || <code>Integrate[(x)^(a - 1)* Gamma[b, 0, x], {x, 0, Infinity}]= -Divide[Gamma[a + b],a]</code> || Failure || Failure || Skip || Error  
 
|-
 
|-
| [https://dlmf.nist.gov/8.14.E4 8.14.E4] || [[Item:Q2637|<math>\int_{0}^{\infty}x^{a-1}\incGamma@{b}{x}\diff{x} = \frac{\EulerGamma@{a+b}}{a}</math>]] || <code>int((x)^(a - 1)* GAMMA(b, x), x = 0..infinity)=(GAMMA(a + b))/(a)</code> || <code>Integrate[(x)^(a - 1)* Gamma[b, x], {x, 0, Infinity}]=Divide[Gamma[a + b],a]</code> || Successful || Failure || - || Successful
+
| [https://dlmf.nist.gov/8.14.E4 8.14.E4] || [[Item:Q2637|<math>\int_{0}^{\infty}x^{a-1}\incGamma@{b}{x}\diff{x} = \frac{\EulerGamma@{a+b}}{a}</math>]] || <code>int((x)^(a - 1)* GAMMA(b, x), x = 0..infinity)=(GAMMA(a + b))/(a)</code> || <code>Integrate[(x)^(a - 1)* Gamma[b, x], {x, 0, Infinity}]=Divide[Gamma[a + b],a]</code> || Successful || Failure || - || Skip
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.14.E5 8.14.E5] || [[Item:Q2638|<math>\int_{0}^{\infty}x^{a-1}e^{-sx}\incgamma@{b}{x}\diff{x} = \frac{\EulerGamma@{a+b}}{b(1+s)^{a+b}}\*\hyperF@{1}{a+b}{1+b}{1/(1+s)}</math>]] || <code>int((x)^(a - 1)* exp(- s*x)*GAMMA(b)-GAMMA(b, x), x = 0..infinity)=(GAMMA(a + b))/(b*(1 + s)^(a + b))* hypergeom([1, a + b], [1 + b], 1/(1 + s))</code> || <code>Integrate[(x)^(a - 1)* Exp[- s*x]*Gamma[b, 0, x], {x, 0, Infinity}]=Divide[Gamma[a + b],b*(1 + s)^(a + b)]* Hypergeometric2F1[1, a + b, 1 + b, 1/(1 + s)]</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/8.14.E5 8.14.E5] || [[Item:Q2638|<math>\int_{0}^{\infty}x^{a-1}e^{-sx}\incgamma@{b}{x}\diff{x} = \frac{\EulerGamma@{a+b}}{b(1+s)^{a+b}}\*\hyperF@{1}{a+b}{1+b}{1/(1+s)}</math>]] || <code>int((x)^(a - 1)* exp(- s*x)*GAMMA(b)-GAMMA(b, x), x = 0..infinity)=(GAMMA(a + b))/(b*(1 + s)^(a + b))* hypergeom([1, a + b], [1 + b], 1/(1 + s))</code> || <code>Integrate[(x)^(a - 1)* Exp[- s*x]*Gamma[b, 0, x], {x, 0, Infinity}]=Divide[Gamma[a + b],b*(1 + s)^(a + b)]* Hypergeometric2F1[1, a + b, 1 + b, 1/(1 + s)]</code> || Failure || Failure || Skip || Error  
Line 231: Line 231:
 
| [https://dlmf.nist.gov/8.14.E6 8.14.E6] || [[Item:Q2639|<math>\int_{0}^{\infty}x^{a-1}e^{-sx}\incGamma@{b}{x}\diff{x} = \frac{\EulerGamma@{a+b}}{a(1+s)^{a+b}}\*\hyperF@{1}{a+b}{1+a}{s/(1+s)}</math>]] || <code>int((x)^(a - 1)* exp(- s*x)*GAMMA(b, x), x = 0..infinity)=(GAMMA(a + b))/(a*(1 + s)^(a + b))* hypergeom([1, a + b], [1 + a], s/(1 + s))</code> || <code>Integrate[(x)^(a - 1)* Exp[- s*x]*Gamma[b, x], {x, 0, Infinity}]=Divide[Gamma[a + b],a*(1 + s)^(a + b)]* Hypergeometric2F1[1, a + b, 1 + a, s/(1 + s)]</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/8.14.E6 8.14.E6] || [[Item:Q2639|<math>\int_{0}^{\infty}x^{a-1}e^{-sx}\incGamma@{b}{x}\diff{x} = \frac{\EulerGamma@{a+b}}{a(1+s)^{a+b}}\*\hyperF@{1}{a+b}{1+a}{s/(1+s)}</math>]] || <code>int((x)^(a - 1)* exp(- s*x)*GAMMA(b, x), x = 0..infinity)=(GAMMA(a + b))/(a*(1 + s)^(a + b))* hypergeom([1, a + b], [1 + a], s/(1 + s))</code> || <code>Integrate[(x)^(a - 1)* Exp[- s*x]*Gamma[b, x], {x, 0, Infinity}]=Divide[Gamma[a + b],a*(1 + s)^(a + b)]* Hypergeometric2F1[1, a + b, 1 + a, s/(1 + s)]</code> || Failure || Failure || Skip || Error  
 
|-
 
|-
| [https://dlmf.nist.gov/8.15.E1 8.15.E1] || [[Item:Q2640|<math>\incgamma@{a}{\lambda x} = \lambda^{a}\sum_{k=0}^{\infty}\incgamma@{a+k}{x}\frac{(1-\lambda)^{k}}{k!}</math>]] || <code>GAMMA(a)-GAMMA(a, lambda*x)= (lambda)^(a)* sum(GAMMA(a + k)-GAMMA(a + k, x)*((1 - lambda)^(k))/(factorial(k)), k = 0..infinity)</code> || <code>Gamma[a, 0, \[Lambda]*x]= (\[Lambda])^(a)* Sum[Gamma[a + k, 0, x]*Divide[(1 - \[Lambda])^(k),(k)!], {k, 0, Infinity}]</code> || Failure || Failure || Skip || Error
+
| [https://dlmf.nist.gov/8.15.E1 8.15.E1] || [[Item:Q2640|<math>\incgamma@{a}{\lambda x} = \lambda^{a}\sum_{k=0}^{\infty}\incgamma@{a+k}{x}\frac{(1-\lambda)^{k}}{k!}</math>]] || <code>GAMMA(a)-GAMMA(a, lambda*x)= (lambda)^(a)* sum(GAMMA(a + k)-GAMMA(a + k, x)*((1 - lambda)^(k))/(factorial(k)), k = 0..infinity)</code> || <code>Gamma[a, 0, \[Lambda]*x]= (\[Lambda])^(a)* Sum[Gamma[a + k, 0, x]*Divide[(1 - \[Lambda])^(k),(k)!], {k, 0, Infinity}]</code> || Failure || Failure || Skip || Skip
 
|-
 
|-
| [https://dlmf.nist.gov/8.17.E1 8.17.E1] || [[Item:Q2641|<math>\incBeta{x}@{a}{b} = \int_{0}^{x}t^{a-1}(1-t)^{b-1}\diff{t}</math>]] || <code>int(t^(a-1)*(1-t)^(b-1), t = 0 .. x)= int((t)^(a - 1)*(1 - t)^(b - 1), t = 0..x)</code> || <code>Beta[x, a, b]= Integrate[(t)^(a - 1)*(1 - t)^(b - 1), {t, 0, x}]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[0, And[Greater[Re[a], 0], Or[LessEqual[Re[x], 1], NotElement[x, Reals]]]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[0, And[Greater[Re[a], 0], Or[LessEqual[Re[x], 1], NotElement[x, Reals]]]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[ConditionalExpression[0, And[Greater[Re[a], 0], Or[LessEqual[Re[x], 1], NotElement[x, Reals]]]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[ConditionalExpression[0, And[Greater[Re[a], 0], Or[LessEqual[Re[x], 1], NotElement[x, Reals]]]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
+
| [https://dlmf.nist.gov/8.17.E1 8.17.E1] || [[Item:Q2641|<math>\incBeta{x}@{a}{b} = \int_{0}^{x}t^{a-1}(1-t)^{b-1}\diff{t}</math>]] || <code>int(t^(a-1)*(1-t)^(b-1), t = 0 .. x)= int((t)^(a - 1)*(1 - t)^(b - 1), t = 0..x)</code> || <code>Beta[x, a, b]= Integrate[(t)^(a - 1)*(1 - t)^(b - 1), {t, 0, x}]</code> || Successful || Failure || - || Skip
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.17.E2 8.17.E2] || [[Item:Q2642|<math>\normincBetaI{x}@{a}{b} = \incBeta{x}@{a}{b}/\EulerBeta@{a}{b}</math>]] || <code>Error</code> || <code>BetaRegularized[x, a, b]= Beta[x, a, b]/ Beta[a, b]</code> || Error || Successful || - || -  
 
| [https://dlmf.nist.gov/8.17.E2 8.17.E2] || [[Item:Q2642|<math>\normincBetaI{x}@{a}{b} = \incBeta{x}@{a}{b}/\EulerBeta@{a}{b}</math>]] || <code>Error</code> || <code>BetaRegularized[x, a, b]= Beta[x, a, b]/ Beta[a, b]</code> || Error || Successful || - || -  
Line 239: Line 239:
 
| [https://dlmf.nist.gov/8.17.E3 8.17.E3] || [[Item:Q2643|<math>\EulerBeta@{a}{b} = \frac{\EulerGamma@{a}\EulerGamma@{b}}{\EulerGamma@{a+b}}</math>]] || <code>Beta(a, b)=(GAMMA(a)*GAMMA(b))/(GAMMA(a + b))</code> || <code>Beta[a, b]=Divide[Gamma[a]*Gamma[b],Gamma[a + b]]</code> || Failure || Successful || Error || -  
 
| [https://dlmf.nist.gov/8.17.E3 8.17.E3] || [[Item:Q2643|<math>\EulerBeta@{a}{b} = \frac{\EulerGamma@{a}\EulerGamma@{b}}{\EulerGamma@{a+b}}</math>]] || <code>Beta(a, b)=(GAMMA(a)*GAMMA(b))/(GAMMA(a + b))</code> || <code>Beta[a, b]=Divide[Gamma[a]*Gamma[b],Gamma[a + b]]</code> || Failure || Successful || Error || -  
 
|-
 
|-
| [https://dlmf.nist.gov/8.17.E4 8.17.E4] || [[Item:Q2644|<math>\normincBetaI{x}@{a}{b} = 1-\normincBetaI{1-x}@{b}{a}</math>]] || <code>Error</code> || <code>BetaRegularized[x, a, b]= 1 - BetaRegularized[1 - x, b, a]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>DirectedInfinity[] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>DirectedInfinity[] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>DirectedInfinity[] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>DirectedInfinity[] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>DirectedInfinity[] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>DirectedInfinity[] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/8.17.E4 8.17.E4] || [[Item:Q2644|<math>\normincBetaI{x}@{a}{b} = 1-\normincBetaI{1-x}@{b}{a}</math>]] || <code>Error</code> || <code>BetaRegularized[x, a, b]= 1 - BetaRegularized[1 - x, b, a]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>DirectedInfinity[] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>DirectedInfinity[] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>DirectedInfinity[] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>DirectedInfinity[] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.17.E5 8.17.E5] || [[Item:Q2645|<math>\normincBetaI{x}@{m}{n-m+1} = \sum_{j=m}^{n}\binom{n}{j}x^{j}(1-x)^{n-j}</math>]] || <code>Error</code> || <code>BetaRegularized[x, m, n - m + 1]= Sum[Binomial[n,j]*(x)^(j)*(1 - x)^(n - j), {j, m, n}]</code> || Error || Failure || - || Successful  
 
| [https://dlmf.nist.gov/8.17.E5 8.17.E5] || [[Item:Q2645|<math>\normincBetaI{x}@{m}{n-m+1} = \sum_{j=m}^{n}\binom{n}{j}x^{j}(1-x)^{n-j}</math>]] || <code>Error</code> || <code>BetaRegularized[x, m, n - m + 1]= Sum[Binomial[n,j]*(x)^(j)*(1 - x)^(n - j), {j, m, n}]</code> || Error || Failure || - || Successful  
Line 249: Line 249:
 
| [https://dlmf.nist.gov/8.17.E8 8.17.E8] || [[Item:Q2648|<math>\incBeta{x}@{a}{b} = \frac{x^{a}(1-x)^{b}}{a}\hyperF@{a+b}{1}{a+1}{x}</math>]] || <code>int(t^(a-1)*(1-t)^(b-1), t = 0 .. x)=((x)^(a)*(1 - x)^(b))/(a)*hypergeom([a + b, 1], [a + 1], x)</code> || <code>Beta[x, a, b]=Divide[(x)^(a)*(1 - x)^(b),a]*Hypergeometric2F1[a + b, 1, a + 1, x]</code> || Failure || Successful || Skip || -  
 
| [https://dlmf.nist.gov/8.17.E8 8.17.E8] || [[Item:Q2648|<math>\incBeta{x}@{a}{b} = \frac{x^{a}(1-x)^{b}}{a}\hyperF@{a+b}{1}{a+1}{x}</math>]] || <code>int(t^(a-1)*(1-t)^(b-1), t = 0 .. x)=((x)^(a)*(1 - x)^(b))/(a)*hypergeom([a + b, 1], [a + 1], x)</code> || <code>Beta[x, a, b]=Divide[(x)^(a)*(1 - x)^(b),a]*Hypergeometric2F1[a + b, 1, a + 1, x]</code> || Failure || Successful || Skip || -  
 
|-
 
|-
| [https://dlmf.nist.gov/8.17.E9 8.17.E9] || [[Item:Q2649|<math>\incBeta{x}@{a}{b} = \frac{x^{a}(1-x)^{b-1}}{a}\hyperF@@{1}{1-b}{a+1}{\frac{x}{x-1}}</math>]] || <code>int(t^(a-1)*(1-t)^(b-1), t = 0 .. x)=((x)^(a)*(1 - x)^(b - 1))/(a)*hypergeom([1, 1 - b], [a + 1], (x)/(x - 1))</code> || <code>Beta[x, a, b]=Divide[(x)^(a)*(1 - x)^(b - 1),a]*Hypergeometric2F1[1, 1 - b, a + 1, Divide[x,x - 1]]</code> || Failure || Failure || Skip || Skip
+
| [https://dlmf.nist.gov/8.17.E9 8.17.E9] || [[Item:Q2649|<math>\incBeta{x}@{a}{b} = \frac{x^{a}(1-x)^{b-1}}{a}\hyperF@@{1}{1-b}{a+1}{\frac{x}{x-1}}</math>]] || <code>int(t^(a-1)*(1-t)^(b-1), t = 0 .. x)=((x)^(a)*(1 - x)^(b - 1))/(a)*hypergeom([1, 1 - b], [a + 1], (x)/(x - 1))</code> || <code>Beta[x, a, b]=Divide[(x)^(a)*(1 - x)^(b - 1),a]*Hypergeometric2F1[1, 1 - b, a + 1, Divide[x,x - 1]]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.27132901967319506, -0.2500814455005845] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[-0.27137899275582306, -0.250091870275464] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[-0.27137899275582306, -0.250091870275464] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[0.08838841600311584, 0.0] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br>... skip entries to safe data<br></div></div>
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.17.E10 8.17.E10] || [[Item:Q2650|<math>\normincBetaI{x}@{a}{b} = \frac{x^{a}(1-x)^{b}}{2\pi i}\int_{c-i\infty}^{c+i\infty}s^{-a}(1-s)^{-b}\frac{\diff{s}}{s-x}</math>]] || <code>Error</code> || <code>BetaRegularized[x, a, b]=Divide[(x)^(a)*(1 - x)^(b),2*Pi*I]*Integrate[(s)^(- a)*(1 - s)^(- b)*Divide[1,s - x], {s, c - I*Infinity, c + I*Infinity}]</code> || Error || Failure || - || Error  
 
| [https://dlmf.nist.gov/8.17.E10 8.17.E10] || [[Item:Q2650|<math>\normincBetaI{x}@{a}{b} = \frac{x^{a}(1-x)^{b}}{2\pi i}\int_{c-i\infty}^{c+i\infty}s^{-a}(1-s)^{-b}\frac{\diff{s}}{s-x}</math>]] || <code>Error</code> || <code>BetaRegularized[x, a, b]=Divide[(x)^(a)*(1 - x)^(b),2*Pi*I]*Integrate[(s)^(- a)*(1 - s)^(- b)*Divide[1,s - x], {s, c - I*Infinity, c + I*Infinity}]</code> || Error || Failure || - || Error  
Line 259: Line 259:
 
| [https://dlmf.nist.gov/8.17.E16 8.17.E16] || [[Item:Q2657|<math>a\normincBetaI{x}@{a+1}{b} = (a+cx)\normincBetaI{x}@{a}{b}-cx\normincBetaI{x}@{a-1}{b}</math>]] || <code>Error</code> || <code>a*BetaRegularized[x, a + 1, b]=(a + c*x)* BetaRegularized[x, a, b]- c*x*BetaRegularized[x, a - 1, b]</code> || Error || Failure || - || Skip  
 
| [https://dlmf.nist.gov/8.17.E16 8.17.E16] || [[Item:Q2657|<math>a\normincBetaI{x}@{a+1}{b} = (a+cx)\normincBetaI{x}@{a}{b}-cx\normincBetaI{x}@{a-1}{b}</math>]] || <code>Error</code> || <code>a*BetaRegularized[x, a + 1, b]=(a + c*x)* BetaRegularized[x, a, b]- c*x*BetaRegularized[x, a - 1, b]</code> || Error || Failure || - || Skip  
 
|-
 
|-
| [https://dlmf.nist.gov/8.17.E24 8.17.E24] || [[Item:Q2666|<math>\normincBetaI{x}@{m}{n} = (1-x)^{n}\sum_{j=m}^{\infty}\binom{n+j-1}{j}x^{j}</math>]] || <code>Error</code> || <code>BetaRegularized[x, m, n]=(1 - x)^(n)* Sum[Binomial[n + j - 1,j]*(x)^(j), {j, m, Infinity}]</code> || Error || Failure || - || Error
+
| [https://dlmf.nist.gov/8.17.E24 8.17.E24] || [[Item:Q2666|<math>\normincBetaI{x}@{m}{n} = (1-x)^{n}\sum_{j=m}^{\infty}\binom{n+j-1}{j}x^{j}</math>]] || <code>Error</code> || <code>BetaRegularized[x, m, n]=(1 - x)^(n)* Sum[Binomial[n + j - 1,j]*(x)^(j), {j, m, Infinity}]</code> || Error || Failure || - || Successful
 
|-
 
|-
| [https://dlmf.nist.gov/8.18.E2 8.18.E2] || [[Item:Q2668|<math>\xi = -\ln@@{x}</math>]] || <code>xi = - ln(x)</code> || <code>\[Xi]= - Log[x]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.414213562+1.414213562*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>2.107360743+1.414213562*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>2.512825851+1.414213562*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>1.414213562-1.414213562*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>2.107360743-1.414213562*I <- {xi = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>2.512825851-1.414213562*I <- {xi = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.414213562-1.414213562*I <- {xi = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-.7210663814-1.414213562*I <- {xi = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.315601273-1.414213562*I <- {xi = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.414213562+1.414213562*I <- {xi = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-.7210663814+1.414213562*I <- {xi = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.315601273+1.414213562*I <- {xi = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.1073607429330403, 1.4142135623730951] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.512825851041205, 1.4142135623730951] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.1073607429330403, -1.4142135623730951] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.512825851041205, -1.4142135623730951] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[x, 1], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.7210663818131499, -1.4142135623730951] <- {Rule[x, 2], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.31560127370498536, -1.4142135623730951] <- {Rule[x, 3], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[x, 1], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.7210663818131499, 1.4142135623730951] <- {Rule[x, 2], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.31560127370498536, 1.4142135623730951] <- {Rule[x, 3], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/8.18.E2 8.18.E2] || [[Item:Q2668|<math>\xi = -\ln@@{x}</math>]] || <code>xi = - ln(x)</code> || <code>\[Xi]= - Log[x]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.414213562+1.414213562*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>2.107360743+1.414213562*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>2.512825851+1.414213562*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>1.414213562-1.414213562*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.1073607429330403, 1.4142135623730951] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.512825851041205, 1.4142135623730951] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
| [https://dlmf.nist.gov/8.18#Ex1 8.18#Ex1] || [[Item:Q2671|<math>F_{0} = a^{-b}\normincGammaQ@{b}{a\xi}</math>]] || <code>F[0]= (a)^(- b)* GAMMA(b, a*xi)/GAMMA(b)</code> || <code>Subscript[F, 0]= (a)^(- b)* GammaRegularized[b, a*\[Xi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>2.106630597+.9392389431*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>2.106630597-1.889188181*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-.7217965272-1.889188181*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-.7217965272+.9392389431*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.314093364+1.422046466*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.314093364-1.406380658*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.514333760-1.406380658*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.514333760+1.422046466*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>37.30078456-.562337051*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>37.30078456-3.390764175*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>34.47235744-3.390764175*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>34.47235744-.562337051*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>-.249187360+.9478787144*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>-.249187360-1.880548410*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.077614484-1.880548410*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.077614484+.9478787144*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>-.772600312-1.812458958*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>-.772600312-4.640886082*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.601027436-4.640886082*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.601027436-1.812458958*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.420114493+1.423367981*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.420114493-1.405059143*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.408312631-1.405059143*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.408312631+1.423367981*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.409716808+1.323260430*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.409716808-1.505166694*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.418710316-1.505166694*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.418710316+1.323260430*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>-2045.501929+409.9986047*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>-2045.501929+407.1701775*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-2048.330357+407.1701775*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-2048.330357+409.9986047*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>-.518247496+.8534804986*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>-.518247496-1.974946625*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.346674620-1.974946625*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.346674620+.8534804986*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.412937466+1.410589353*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.412937466-1.417837771*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.415489658-1.417837771*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.415489658+1.410589353*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.439296879+1.387205133*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.439296879-1.441221991*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.389130245-1.441221991*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.389130245+1.387205133*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>-1087.634663-1744.506372*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>-1087.634663-1747.334800*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1090.463091-1747.334800*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1090.463091-1744.506372*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.075970282+1.447404288*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.075970282-1.381022836*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.752456842-1.381022836*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.752456842+1.447404288*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.394750444+1.384610194*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.394750444-1.443816930*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.433676680-1.443816930*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.433676680+1.384610194*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>8.092886871-15.89547698*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>8.092886871-18.72390410*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>5.264459747-18.72390410*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>5.264459747-15.89547698*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>-7.071803294+2.944767786*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>-7.071803294+.116340662*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-9.900230418+.116340662*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-9.900230418+2.944767786*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.420114493+1.405059143*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.420114493-1.423367981*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.408312631-1.423367981*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.408312631+1.405059143*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>-.772600312+4.640886082*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>-.772600312+1.812458958*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.601027436+1.812458958*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.601027436+4.640886082*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.563724365+1.301303726*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.563724365-1.527123398*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.264702759-1.527123398*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.264702759+1.301303726*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.409716808+1.505166694*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.409716808-1.323260430*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.418710316-1.323260430*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.418710316+1.505166694*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.314093364+1.406380658*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.314093364-1.422046466*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.514333760-1.422046466*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.514333760+1.406380658*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>2.106630597+1.889188181*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>2.106630597-.9392389431*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-.7217965272-.9392389431*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-.7217965272+1.889188181*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>8435.591579-17298.26921*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>8435.591579-17301.09763*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>8432.763151-17301.09763*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>8432.763151-17298.26921*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>37.30078456+3.390764175*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>37.30078456+.562337051*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>34.47235744+.562337051*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>34.47235744+3.390764175*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.394750444+1.443816930*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.394750444-1.384610194*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.433676680-1.384610194*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.433676680+1.443816930*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.075970282+1.381022836*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.075970282-1.447404288*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.752456842-1.447404288*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.752456842+1.381022836*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>-6725.763784+17742.35818*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>-6725.763784+17739.52976*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-6728.592212+17739.52976*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-6728.592212+17742.35818*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>8.092886871+18.72390410*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>8.092886871+15.89547698*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>5.264459747+15.89547698*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>5.264459747+18.72390410*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.412937466+1.417837771*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.412937466-1.410589353*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.415489658-1.410589353*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.415489658+1.417837771*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>-.518247496+1.974946625*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>-.518247496-.8534804986*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.346674620-.8534804986*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.346674620+1.974946625*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>2.103737263+2.045973050*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>2.103737263-.7824540745*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-.7246898606-.7824540745*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-.7246898606+2.045973050*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.439296879+1.441221991*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.439296879-1.387205133*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.389130245-1.387205133*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.389130245+1.441221991*I <- {a = 2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.279418990+1.013542994*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.279418990-1.814884130*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.549008134-1.814884130*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.549008134+1.013542994*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.414135792+1.434532625*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.414135792-1.393894499*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.414291332-1.393894499*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.414291332+1.434532625*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.406660148+1.407850824*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.406660148-1.420576300*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.421766976-1.420576300*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.421766976+1.407850824*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.414615912+1.415324135*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.414615912-1.413102989*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.413811212-1.413102989*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.413811212+1.415324135*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.937666460+3.841627073*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.937666460+1.013199949*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-8.766093584+1.013199949*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-8.766093584+3.841627073*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>79821.12535+158498.5202*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>79821.12535+158495.6918*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>79818.29693+158495.6918*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>79818.29693+158498.5202*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>-213.5110642+253.6671586*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>-213.5110642+250.8387314*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-216.3394914+250.8387314*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-216.3394914+253.6671586*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>2.030845520+.7233999937*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>2.030845520-2.105027130*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-.7975816042-2.105027130*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-.7975816042+.7233999937*I <- {a = -2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>3.059763483+4.081197323*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>3.059763483+1.252770199*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>.231336359+1.252770199*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>.231336359+4.081197323*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>167733.5702-49724.58926*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>167733.5702-49727.41768*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>167730.7418-49727.41768*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>167730.7418-49724.58926*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>91.11170102-144.2590366*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>91.11170102-147.0874638*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>88.28327390-147.0874638*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>88.28327390-144.2590366*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.740106954+1.391677602*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.740106954-1.436749522*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.088320170-1.436749522*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.088320170+1.391677602*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.589544961+1.544140959*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.589544961-1.284286165*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.238882163-1.284286165*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.238882163+1.544140959*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.423436628+1.313210949*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.423436628-1.515216175*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.404990496-1.515216175*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.404990496+1.313210949*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.414896539+1.410274819*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.414896539-1.418152305*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.413530585-1.418152305*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.413530585+1.410274819*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.414610140+1.414085609*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.414610140-1.414341515*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.413816984-1.414341515*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.413816984+1.414085609*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>7.282785335+16.22266258*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>7.282785335+13.39423546*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>4.454358211+13.39423546*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>4.454358211+16.22266258*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.937666460-1.013199949*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.937666460-3.841627073*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-8.766093584-3.841627073*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-8.766093584-1.013199949*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>2.030845520+2.105027130*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>2.030845520-.7233999937*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-.7975816042-.7233999937*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-.7975816042+2.105027130*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>-213.5110642-250.8387314*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>-213.5110642-253.6671586*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-216.3394914-253.6671586*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-216.3394914-250.8387314*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>171.1344632+151.2131284*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>171.1344632+148.3847012*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>168.3060360+148.3847012*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>168.3060360+151.2131284*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.279418990+1.814884130*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.279418990-1.013542994*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.549008134-1.013542994*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.549008134+1.814884130*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.414615912+1.413102989*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.414615912-1.415324135*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.413811212-1.415324135*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.413811212+1.413102989*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.406660148+1.420576300*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.406660148-1.407850824*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.421766976-1.407850824*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.421766976+1.420576300*I <- {a = -2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>223.6178792+22.12380068*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>223.6178792+19.29537356*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>220.7894520+19.29537356*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>220.7894520+22.12380068*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.589544961+1.284286165*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.589544961-1.544140959*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.238882163-1.544140959*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.238882163+1.284286165*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.414610140+1.414341515*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.414610140-1.414085609*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.413816984-1.414085609*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.413816984+1.414341515*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.414896539+1.418152305*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.414896539-1.410274819*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.413530585-1.410274819*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.413530585+1.418152305*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>37.57863319-69.39384278*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>37.57863319-72.22226990*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>34.75020607-72.22226990*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>34.75020607-69.39384278*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>3.059763483-1.252770199*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>3.059763483-4.081197323*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>.231336359-4.081197323*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>.231336359-1.252770199*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.740106954+1.436749522*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.740106954-1.391677602*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.088320170-1.391677602*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.088320170+1.436749522*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br><code>91.11170102+147.0874638*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>91.11170102+144.2590366*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>88.28327390+144.2590366*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>88.28327390+147.0874638*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || Skip  
+
| [https://dlmf.nist.gov/8.18#Ex1 8.18#Ex1] || [[Item:Q2671|<math>F_{0} = a^{-b}\normincGammaQ@{b}{a\xi}</math>]] || <code>F[0]= (a)^(- b)* GAMMA(b, a*xi)/GAMMA(b)</code> || <code>Subscript[F, 0]= (a)^(- b)* GammaRegularized[b, a*\[Xi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>2.106630597+.9392389431*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}</code><br><code>2.106630597-1.889188181*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}</code><br><code>-.7217965272-1.889188181*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}</code><br><code>-.7217965272+.9392389431*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Skip  
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.18#Ex2 8.18#Ex2] || [[Item:Q2672|<math>F_{1} = \frac{b-a\xi}{a}F_{0}+\frac{\xi^{b}e^{-a\xi}}{a\EulerGamma@{b}}</math>]] || <code>F[1]=(b - a*xi)/(a)*F[0]+((xi)^(b)* exp(- a*xi))/(a*GAMMA(b))</code> || <code>Subscript[F, 1]=Divide[b - a*\[Xi],a]*Subscript[F, 0]+Divide[(\[Xi])^(b)* Exp[- a*\[Xi]],a*Gamma[b]]</code> || Failure || Failure || Skip || Skip  
 
| [https://dlmf.nist.gov/8.18#Ex2 8.18#Ex2] || [[Item:Q2672|<math>F_{1} = \frac{b-a\xi}{a}F_{0}+\frac{\xi^{b}e^{-a\xi}}{a\EulerGamma@{b}}</math>]] || <code>F[1]=(b - a*xi)/(a)*F[0]+((xi)^(b)* exp(- a*xi))/(a*GAMMA(b))</code> || <code>Subscript[F, 1]=Divide[b - a*\[Xi],a]*Subscript[F, 0]+Divide[(\[Xi])^(b)* Exp[- a*\[Xi]],a*Gamma[b]]</code> || Failure || Failure || Skip || Skip  
 
|-
 
|-
| [https://dlmf.nist.gov/8.18.E10 8.18.E10] || [[Item:Q2678|<math>-\tfrac{1}{2}\eta^{2} = x_{0}\ln@{\frac{x}{x_{0}}}+(1-x_{0})\ln@{\frac{1-x}{1-x_{0}}}</math>]] || <code>-(1)/(2)*(eta)^(2)= x[0]*ln((x)/(x[0]))+(1 - x[0])* ln((1 - x)/(1 - x[0]))</code> || <code>-Divide[1,2]*(\[Eta])^(2)= Subscript[x, 0]*Log[Divide[x,Subscript[x, 0]]]+(1 - Subscript[x, 0])* Log[Divide[1 - x,1 - Subscript[x, 0]]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Float(undefined)-Float(infinity)*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>.547175857-1.970232147*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.260872566-1.563388258*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(undefined)+Float(infinity)*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>.547175857-2.029767851*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>.260872566-2.436611740*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>2.845263019-3.517957696*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>1.745271949-3.924801585*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>2.845263019-.482042302*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>1.745271949-.75198413e-1*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(undefined)-Float(infinity)*I <- {eta = 2^(1/2)-I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>.547175857+2.029767851*I <- {eta = 2^(1/2)-I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.260872566+2.436611740*I <- {eta = 2^(1/2)-I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(undefined)+Float(infinity)*I <- {eta = 2^(1/2)-I*2^(1/2), x[0] = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>.547175857+1.970232147*I <- {eta = 2^(1/2)-I*2^(1/2), x[0] = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>.260872566+1.563388258*I <- {eta = 2^(1/2)-I*2^(1/2), x[0] = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {eta = 2^(1/2)-I*2^(1/2), x[0] = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>2.845263019+.482042302*I <- {eta = 2^(1/2)-I*2^(1/2), x[0] = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>1.745271949+.75198413e-1*I <- {eta = 2^(1/2)-I*2^(1/2), x[0] = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {eta = 2^(1/2)-I*2^(1/2), x[0] = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>2.845263019+3.517957696*I <- {eta = 2^(1/2)-I*2^(1/2), x[0] = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>1.745271949+3.924801585*I <- {eta = 2^(1/2)-I*2^(1/2), x[0] = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(undefined)-Float(infinity)*I <- {eta = -2^(1/2)-I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>.547175857-1.970232147*I <- {eta = -2^(1/2)-I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.260872566-1.563388258*I <- {eta = -2^(1/2)-I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(undefined)+Float(infinity)*I <- {eta = -2^(1/2)-I*2^(1/2), x[0] = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>.547175857-2.029767851*I <- {eta = -2^(1/2)-I*2^(1/2), x[0] = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>.260872566-2.436611740*I <- {eta = -2^(1/2)-I*2^(1/2), x[0] = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {eta = -2^(1/2)-I*2^(1/2), x[0] = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>2.845263019-3.517957696*I <- {eta = -2^(1/2)-I*2^(1/2), x[0] = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>1.745271949-3.924801585*I <- {eta = -2^(1/2)-I*2^(1/2), x[0] = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {eta = -2^(1/2)-I*2^(1/2), x[0] = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>2.845263019-.482042302*I <- {eta = -2^(1/2)-I*2^(1/2), x[0] = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>1.745271949-.75198413e-1*I <- {eta = -2^(1/2)-I*2^(1/2), x[0] = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(undefined)-Float(infinity)*I <- {eta = -2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>.547175857+2.029767851*I <- {eta = -2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.260872566+2.436611740*I <- {eta = -2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(undefined)+Float(infinity)*I <- {eta = -2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>.547175857+1.970232147*I <- {eta = -2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>.260872566+1.563388258*I <- {eta = -2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {eta = -2^(1/2)+I*2^(1/2), x[0] = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>2.845263019+.482042302*I <- {eta = -2^(1/2)+I*2^(1/2), x[0] = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>1.745271949+.75198413e-1*I <- {eta = -2^(1/2)+I*2^(1/2), x[0] = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {eta = -2^(1/2)+I*2^(1/2), x[0] = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>2.845263019+3.517957696*I <- {eta = -2^(1/2)+I*2^(1/2), x[0] = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>1.745271949+3.924801585*I <- {eta = -2^(1/2)+I*2^(1/2), x[0] = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || Successful  
+
| [https://dlmf.nist.gov/8.18.E10 8.18.E10] || [[Item:Q2678|<math>-\tfrac{1}{2}\eta^{2} = x_{0}\ln@{\frac{x}{x_{0}}}+(1-x_{0})\ln@{\frac{1-x}{1-x_{0}}}</math>]] || <code>-(1)/(2)*(eta)^(2)= x[0]*ln((x)/(x[0]))+(1 - x[0])* ln((1 - x)/(1 - x[0]))</code> || <code>-Divide[1,2]*(\[Eta])^(2)= Subscript[x, 0]*Log[Divide[x,Subscript[x, 0]]]+(1 - Subscript[x, 0])* Log[Divide[1 - x,1 - Subscript[x, 0]]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Float(undefined)-Float(infinity)*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>.547175857-1.970232147*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.260872566-1.563388258*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(undefined)+Float(infinity)*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)-I*2^(1/2), x = 1}</code><br>... skip entries to safe data<br></div></div> || Successful  
 
|-
 
|-
| [https://dlmf.nist.gov/8.18.E15 8.18.E15] || [[Item:Q2683|<math>\mu\ln@@{\zeta}-\zeta = \ln@@{x}+\mu\ln@{1-x}+(1+\mu)\ln@{1+\mu}-\mu</math>]] || <code>mu*ln(zeta)- zeta = ln(x)+ mu*ln(1 - x)+(1 + mu)* ln(1 + mu)- mu</code> || <code>\[Mu]*Log[\[zeta]]- \[zeta]= Log[x]+ \[Mu]*Log[1 - x]+(1 + \[Mu])* Log[1 + \[Mu]]- \[Mu]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Float(infinity)+Float(infinity)*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>1.884730882-5.086259752*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.499007630-6.066517895*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>4.106172350-4.479274096*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>2.720449098-5.459532239*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>9.156040946-6.700715565*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>7.770317690-7.680973708*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>2.491716537-2.864818284*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>1.105993285-3.845076427*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = 2^(1/2)-I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-4.779593526-4.406491780*I <- {mu = 2^(1/2)-I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-6.165316777-3.426233636*I <- {mu = 2^(1/2)-I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = 2^(1/2)-I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-7.001034994-3.799506124*I <- {mu = 2^(1/2)-I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-8.386758245-2.819247980*I <- {mu = 2^(1/2)-I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = 2^(1/2)-I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-6.394049339-6.020947592*I <- {mu = 2^(1/2)-I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-7.779772590-5.040689448*I <- {mu = 2^(1/2)-I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = 2^(1/2)-I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>.270275066-2.185050311*I <- {mu = 2^(1/2)-I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-1.115448185-1.204792167*I <- {mu = 2^(1/2)-I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = -2^(1/2)-I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-5.049008308-.6968604642*I <- {mu = -2^(1/2)-I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-4.474215272+.2833976788*I <- {mu = -2^(1/2)-I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = -2^(1/2)-I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-7.270449776+4.353008128*I <- {mu = -2^(1/2)-I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-6.695656740+5.333266271*I <- {mu = -2^(1/2)-I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = -2^(1/2)-I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-6.663464120+6.574449597*I <- {mu = -2^(1/2)-I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-6.088671084+7.554707740*I <- {mu = -2^(1/2)-I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = -2^(1/2)-I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>.860285e-3-2.918301932*I <- {mu = -2^(1/2)-I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.575653321-1.938043789*I <- {mu = -2^(1/2)-I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = -2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>1.615316100+4.532757748*I <- {mu = -2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>2.190109135+3.552499604*I <- {mu = -2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = -2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>3.836757568+9.582626340*I <- {mu = -2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>4.411550603+8.602368196*I <- {mu = -2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = -2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>8.886626161+11.80406781*I <- {mu = -2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>9.461419196+10.82380966*I <- {mu = -2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = -2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>2.222301756+2.311316279*I <- {mu = -2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>2.797094791+1.331058135*I <- {mu = -2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || Error  
+
| [https://dlmf.nist.gov/8.18.E15 8.18.E15] || [[Item:Q2683|<math>\mu\ln@@{\zeta}-\zeta = \ln@@{x}+\mu\ln@{1-x}+(1+\mu)\ln@{1+\mu}-\mu</math>]] || <code>mu*ln(zeta)- zeta = ln(x)+ mu*ln(1 - x)+(1 + mu)* ln(1 + mu)- mu</code> || <code>\[Mu]*Log[\[zeta]]- \[zeta]= Log[x]+ \[Mu]*Log[1 - x]+(1 + \[Mu])* Log[1 + \[Mu]]- \[Mu]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Float(infinity)+Float(infinity)*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>1.884730882-5.086259752*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.499007630-6.066517895*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 1}</code><br>... skip entries to safe data<br></div></div> || Error  
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.18.E18 8.18.E18] || [[Item:Q2686|<math>\normincBetaI{x}@{a}{b} = p</math>]] || <code>Error</code> || <code>BetaRegularized[x, a, b]= p</code> || Error || Failure || - || Successful  
 
| [https://dlmf.nist.gov/8.18.E18 8.18.E18] || [[Item:Q2686|<math>\normincBetaI{x}@{a}{b} = p</math>]] || <code>Error</code> || <code>BetaRegularized[x, a, b]= p</code> || Error || Failure || - || Successful  
Line 285: Line 285:
 
| [https://dlmf.nist.gov/8.19.E6 8.19.E6] || [[Item:Q2692|<math>\genexpintE{p}@{0} = \frac{1}{p-1}</math>]] || <code>Ei(p, 0)=(1)/(p - 1)</code> || <code>ExpIntegralE[p, 0]=Divide[1,p - 1]</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/8.19.E6 8.19.E6] || [[Item:Q2692|<math>\genexpintE{p}@{0} = \frac{1}{p-1}</math>]] || <code>Ei(p, 0)=(1)/(p - 1)</code> || <code>ExpIntegralE[p, 0]=Divide[1,p - 1]</code> || Successful || Successful || - || -  
 
|-
 
|-
| [https://dlmf.nist.gov/8.19.E7 8.19.E7] || [[Item:Q2693|<math>\genexpintE{n}@{z} = \frac{(-z)^{n-1}}{(n-1)!}\expintE@{z}+\frac{e^{-z}}{(n-1)!}\sum_{k=0}^{n-2}(n-k-2)!(-z)^{k}</math>]] || <code>Ei(n, z)=((- z)^(n - 1))/(factorial(n - 1))*Ei(z)+(exp(- z))/(factorial(n - 1))*sum(factorial(n - k - 2)*(- z)^(k), k = 0..n - 2)</code> || <code>ExpIntegralE[n, z]=Divide[(- z)^(n - 1),(n - 1)!]*-ExpIntegralEi[-(z)]+Divide[Exp[- z],(n - 1)!]*Sum[(n - k - 2)!*(- z)^(k), {k, 0, n - 2}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.0, -3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.442882938158367, 4.442882938158366] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.283185307179586, 0.0] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.442882938158367, -4.442882938158366] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.283185307179586, 0.0] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.442882938158366, 4.442882938158366] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.283185307179586, 0.0] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.442882938158366, -4.442882938158366] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.283185307179586, 0.0] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/8.19.E7 8.19.E7] || [[Item:Q2693|<math>\genexpintE{n}@{z} = \frac{(-z)^{n-1}}{(n-1)!}\expintE@{z}+\frac{e^{-z}}{(n-1)!}\sum_{k=0}^{n-2}(n-k-2)!(-z)^{k}</math>]] || <code>Ei(n, z)=((- z)^(n - 1))/(factorial(n - 1))*Ei(z)+(exp(- z))/(factorial(n - 1))*sum(factorial(n - k - 2)*(- z)^(k), k = 0..n - 2)</code> || <code>ExpIntegralE[n, z]=Divide[(- z)^(n - 1),(n - 1)!]*-ExpIntegralEi[-(z)]+Divide[Exp[- z],(n - 1)!]*Sum[(n - k - 2)!*(- z)^(k), {k, 0, n - 2}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.0, -3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.442882938158367, 4.442882938158366] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.283185307179586, 0.0] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
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| [https://dlmf.nist.gov/8.19.E9 8.19.E9] || [[Item:Q2695|<math>\genexpintE{n}@{z} = \frac{(-1)^{n}z^{n-1}}{(n-1)!}\ln@@{z}+\frac{e^{-z}}{(n-1)!}\sum_{k=1}^{n-1}(-z)^{k-1}\EulerGamma@{n-k}+\frac{e^{-z}(-z)^{n-1}}{(n-1)!}\sum_{k=0}^{\infty}\frac{z^{k}}{k!}\digamma@{k+1}</math>]] || <code>Ei(n, z)=((- 1)^(n)* (z)^(n - 1))/(factorial(n - 1))*ln(z)+(exp(- z))/(factorial(n - 1))*sum((- z)^(k - 1)* GAMMA(n - k), k = 1..n - 1)+(exp(- z)*(- z)^(n - 1))/(factorial(n - 1))*sum(((z)^(k))/(factorial(k))*Psi(k + 1), k = 0..infinity)</code> || <code>ExpIntegralE[n, z]=Divide[(- 1)^(n)* (z)^(n - 1),(n - 1)!]*Log[z]+Divide[Exp[- z],(n - 1)!]*Sum[(- z)^(k - 1)* Gamma[n - k], {k, 1, n - 1}]+Divide[Exp[- z]*(- z)^(n - 1),(n - 1)!]*Sum[Divide[(z)^(k),(k)!]*PolyGamma[k + 1], {k, 0, Infinity}]</code> || Error || Failure || - || Successful  
 
| [https://dlmf.nist.gov/8.19.E9 8.19.E9] || [[Item:Q2695|<math>\genexpintE{n}@{z} = \frac{(-1)^{n}z^{n-1}}{(n-1)!}\ln@@{z}+\frac{e^{-z}}{(n-1)!}\sum_{k=1}^{n-1}(-z)^{k-1}\EulerGamma@{n-k}+\frac{e^{-z}(-z)^{n-1}}{(n-1)!}\sum_{k=0}^{\infty}\frac{z^{k}}{k!}\digamma@{k+1}</math>]] || <code>Ei(n, z)=((- 1)^(n)* (z)^(n - 1))/(factorial(n - 1))*ln(z)+(exp(- z))/(factorial(n - 1))*sum((- z)^(k - 1)* GAMMA(n - k), k = 1..n - 1)+(exp(- z)*(- z)^(n - 1))/(factorial(n - 1))*sum(((z)^(k))/(factorial(k))*Psi(k + 1), k = 0..infinity)</code> || <code>ExpIntegralE[n, z]=Divide[(- 1)^(n)* (z)^(n - 1),(n - 1)!]*Log[z]+Divide[Exp[- z],(n - 1)!]*Sum[(- z)^(k - 1)* Gamma[n - k], {k, 1, n - 1}]+Divide[Exp[- z]*(- z)^(n - 1),(n - 1)!]*Sum[Divide[(z)^(k),(k)!]*PolyGamma[k + 1], {k, 0, Infinity}]</code> || Error || Failure || - || Successful  
Line 317: Line 317:
 
| [https://dlmf.nist.gov/8.19.E23 8.19.E23] || [[Item:Q2709|<math>\int_{z}^{\infty}\genexpintE{p-1}@{t}\diff{t} = \genexpintE{p}@{z}</math>]] || <code>int(Ei(p - 1, t), t = z..infinity)= Ei(p, z)</code> || <code>Integrate[ExpIntegralE[p - 1, t], {t, z, Infinity}]= ExpIntegralE[p, z]</code> || Failure || Failure || Skip || Successful  
 
| [https://dlmf.nist.gov/8.19.E23 8.19.E23] || [[Item:Q2709|<math>\int_{z}^{\infty}\genexpintE{p-1}@{t}\diff{t} = \genexpintE{p}@{z}</math>]] || <code>int(Ei(p - 1, t), t = z..infinity)= Ei(p, z)</code> || <code>Integrate[ExpIntegralE[p - 1, t], {t, z, Infinity}]= ExpIntegralE[p, z]</code> || Failure || Failure || Skip || Successful  
 
|-
 
|-
| [https://dlmf.nist.gov/8.19.E24 8.19.E24] || [[Item:Q2710|<math>\int_{0}^{\infty}e^{-at}\genexpintE{n}@{t}\diff{t} = \frac{(-1)^{n-1}}{a^{n}}\left(\ln@{1+a}+\sum_{k=1}^{n-1}\frac{(-1)^{k}a^{k}}{k}\right)</math>]] || <code>int(exp(- a*t)*Ei(n, t), t = 0..infinity)=((- 1)^(n - 1))/((a)^(n))*(ln(1 + a)+ sum(((- 1)^(k)* (a)^(k))/(k), k = 1..n - 1))</code> || <code>Integrate[Exp[- a*t]*ExpIntegralE[n, t], {t, 0, Infinity}]=Divide[(- 1)^(n - 1),(a)^(n)]*(Log[1 + a]+ Sum[Divide[(- 1)^(k)* (a)^(k),k], {k, 1, n - 1}])</code> || Failure || Failure || Skip || Error
+
| [https://dlmf.nist.gov/8.19.E24 8.19.E24] || [[Item:Q2710|<math>\int_{0}^{\infty}e^{-at}\genexpintE{n}@{t}\diff{t} = \frac{(-1)^{n-1}}{a^{n}}\left(\ln@{1+a}+\sum_{k=1}^{n-1}\frac{(-1)^{k}a^{k}}{k}\right)</math>]] || <code>int(exp(- a*t)*Ei(n, t), t = 0..infinity)=((- 1)^(n - 1))/((a)^(n))*(ln(1 + a)+ sum(((- 1)^(k)* (a)^(k))/(k), k = 1..n - 1))</code> || <code>Integrate[Exp[- a*t]*ExpIntegralE[n, t], {t, 0, Infinity}]=Divide[(- 1)^(n - 1),(a)^(n)]*(Log[1 + a]+ Sum[Divide[(- 1)^(k)* (a)^(k),k], {k, 1, n - 1}])</code> || Failure || Failure || Skip || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.19.E25 8.19.E25] || [[Item:Q2711|<math>\int_{0}^{\infty}e^{-at}t^{b-1}\genexpintE{p}@{t}\diff{t} = \frac{\EulerGamma@{b}(1+a)^{-b}}{p+b-1}\*\hyperF@{1}{b}{p+b}{a/(1+a)}</math>]] || <code>int(exp(- a*t)*(t)^(b - 1)* Ei(p, t), t = 0..infinity)=(GAMMA(b)*(1 + a)^(- b))/(p + b - 1)* hypergeom([1, b], [p + b], a/(1 + a))</code> || <code>Integrate[Exp[- a*t]*(t)^(b - 1)* ExpIntegralE[p, t], {t, 0, Infinity}]=Divide[Gamma[b]*(1 + a)^(- b),p + b - 1]* Hypergeometric2F1[1, b, p + b, a/(1 + a)]</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/8.19.E25 8.19.E25] || [[Item:Q2711|<math>\int_{0}^{\infty}e^{-at}t^{b-1}\genexpintE{p}@{t}\diff{t} = \frac{\EulerGamma@{b}(1+a)^{-b}}{p+b-1}\*\hyperF@{1}{b}{p+b}{a/(1+a)}</math>]] || <code>int(exp(- a*t)*(t)^(b - 1)* Ei(p, t), t = 0..infinity)=(GAMMA(b)*(1 + a)^(- b))/(p + b - 1)* hypergeom([1, b], [p + b], a/(1 + a))</code> || <code>Integrate[Exp[- a*t]*(t)^(b - 1)* ExpIntegralE[p, t], {t, 0, Infinity}]=Divide[Gamma[b]*(1 + a)^(- b),p + b - 1]* Hypergeometric2F1[1, b, p + b, a/(1 + a)]</code> || Failure || Failure || Skip || Error  
 
|-
 
|-
| [https://dlmf.nist.gov/8.19.E26 8.19.E26] || [[Item:Q2712|<math>\int_{0}^{\infty}\genexpintE{p}@{t}\genexpintE{q}@{t}\diff{t} = \frac{L(p)+L(q)}{p+q-1}</math>]] || <code>int(Ei(p, t)*Ei(q, t), t = 0..infinity)=(L*(p)+ L*(q))/(p + q - 1)</code> || <code>Integrate[ExpIntegralE[p, t]*ExpIntegralE[q, t], {t, 0, Infinity}]=Divide[L*(p)+ L*(q),p + q - 1]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-1.9874359859908697, -2.1876726427121085] <- {Rule[L, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.9874359859908697, -2.1876726427121085] <- {Rule[L, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.9874359859908697, 2.1876726427121085] <- {Rule[L, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.9874359859908697, 2.1876726427121085] <- {Rule[L, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.3879092994333475, 2.1876726427121085] <- {Rule[L, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.3879092994333475, 2.1876726427121085] <- {Rule[L, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.3879092994333475, -2.1876726427121085] <- {Rule[L, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.3879092994333475, -2.1876726427121085] <- {Rule[L, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/8.19.E26 8.19.E26] || [[Item:Q2712|<math>\int_{0}^{\infty}\genexpintE{p}@{t}\genexpintE{q}@{t}\diff{t} = \frac{L(p)+L(q)}{p+q-1}</math>]] || <code>int(Ei(p, t)*Ei(q, t), t = 0..infinity)=(L*(p)+ L*(q))/(p + q - 1)</code> || <code>Integrate[ExpIntegralE[p, t]*ExpIntegralE[q, t], {t, 0, Infinity}]=Divide[L*(p)+ L*(q),p + q - 1]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-1.9874359859908697, -2.1876726427121085] <- {Rule[L, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.9874359859908697, -2.1876726427121085] <- {Rule[L, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.9874359859908697, 2.1876726427121085] <- {Rule[L, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.9874359859908697, 2.1876726427121085] <- {Rule[L, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
| [https://dlmf.nist.gov/8.19.E27 8.19.E27] || [[Item:Q2713|<math>L(p) = \int_{0}^{\infty}e^{-t}\genexpintE{p}@{t}\diff{t}</math>]] || <code>L*(p)= int(exp(- t)*Ei(p, t), t = 0..infinity)</code> || <code>L*(p)= Integrate[Exp[- t]*ExpIntegralE[p, t], {t, 0, Infinity}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[p, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[L, p], Times[Rational[1, 2], Plus[PolyGamma[0, Times[Rational[1, 2], p]], Times[-1, PolyGamma[0, Times[Rational[1, 2], Plus[1, p]]]]]]], Greater[Re[p], 0]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[p, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[L, p], Times[Rational[1, 2], Plus[PolyGamma[0, Times[Rational[1, 2], p]], Times[-1, PolyGamma[0, Times[Rational[1, 2], Plus[1, p]]]]]]], Greater[Re[p], 0]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[p, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[L, p], Times[Rational[1, 2], Plus[PolyGamma[0, Times[Rational[1, 2], p]], Times[-1, PolyGamma[0, Times[Rational[1, 2], Plus[1, p]]]]]]], Greater[Re[p], 0]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[p, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[L, p], Times[Rational[1, 2], Plus[PolyGamma[0, Times[Rational[1, 2], p]], Times[-1, PolyGamma[0, Times[Rational[1, 2], Plus[1, p]]]]]]], Greater[Re[p], 0]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
+
| [https://dlmf.nist.gov/8.19.E27 8.19.E27] || [[Item:Q2713|<math>L(p) = \int_{0}^{\infty}e^{-t}\genexpintE{p}@{t}\diff{t}</math>]] || <code>L*(p)= int(exp(- t)*Ei(p, t), t = 0..infinity)</code> || <code>L*(p)= Integrate[Exp[- t]*ExpIntegralE[p, t], {t, 0, Infinity}]</code> || Failure || Failure || Skip || Skip
 
|-
 
|-
| [https://dlmf.nist.gov/8.19.E27 8.19.E27] || [[Item:Q2713|<math>\int_{0}^{\infty}e^{-t}\genexpintE{p}@{t}\diff{t} = \frac{1}{2p}\hyperF@{1}{1}{1+p}{\tfrac{1}{2}}</math>]] || <code>int(exp(- t)*Ei(p, t), t = 0..infinity)=(1)/(2*p)*hypergeom([1, 1], [1 + p], (1)/(2))</code> || <code>Integrate[Exp[- t]*ExpIntegralE[p, t], {t, 0, Infinity}]=Divide[1,2*p]*Hypergeometric2F1[1, 1, 1 + p, Divide[1,2]]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[p, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[Rational[1, 2], Plus[Times[-1, PolyGamma[0, Plus[Rational[1, 2], Times[Rational[1, 2], p]]]], PolyGamma[0, Times[Rational[1, 2], p]]]], Times[Rational[1, 2], Plus[Times[-1, PolyGamma[0, Times[Rational[1, 2], p]]], PolyGamma[0, Times[Rational[1, 2], Plus[1, p]]]]]], Greater[Re[p], 0]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[p, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[Rational[1, 2], Plus[Times[-1, PolyGamma[0, Plus[Rational[1, 2], Times[Rational[1, 2], p]]]], PolyGamma[0, Times[Rational[1, 2], p]]]], Times[Rational[1, 2], Plus[Times[-1, PolyGamma[0, Times[Rational[1, 2], p]]], PolyGamma[0, Times[Rational[1, 2], Plus[1, p]]]]]], Greater[Re[p], 0]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[p, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[Rational[1, 2], Plus[Times[-1, PolyGamma[0, Plus[Rational[1, 2], Times[Rational[1, 2], p]]]], PolyGamma[0, Times[Rational[1, 2], p]]]], Times[Rational[1, 2], Plus[Times[-1, PolyGamma[0, Times[Rational[1, 2], p]]], PolyGamma[0, Times[Rational[1, 2], Plus[1, p]]]]]], Greater[Re[p], 0]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[p, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[Rational[1, 2], Plus[Times[-1, PolyGamma[0, Plus[Rational[1, 2], Times[Rational[1, 2], p]]]], PolyGamma[0, Times[Rational[1, 2], p]]]], Times[Rational[1, 2], Plus[Times[-1, PolyGamma[0, Times[Rational[1, 2], p]]], PolyGamma[0, Times[Rational[1, 2], Plus[1, p]]]]]], Greater[Re[p], 0]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
+
| [https://dlmf.nist.gov/8.19.E27 8.19.E27] || [[Item:Q2713|<math>\int_{0}^{\infty}e^{-t}\genexpintE{p}@{t}\diff{t} = \frac{1}{2p}\hyperF@{1}{1}{1+p}{\tfrac{1}{2}}</math>]] || <code>int(exp(- t)*Ei(p, t), t = 0..infinity)=(1)/(2*p)*hypergeom([1, 1], [1 + p], (1)/(2))</code> || <code>Integrate[Exp[- t]*ExpIntegralE[p, t], {t, 0, Infinity}]=Divide[1,2*p]*Hypergeometric2F1[1, 1, 1 + p, Divide[1,2]]</code> || Failure || Failure || Skip || Skip
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.20.E1 8.20.E1] || [[Item:Q2714|<math>\genexpintE{p}@{z} = \frac{e^{-z}}{z}\left(\sum_{k=0}^{n-1}(-1)^{k}\frac{\Pochhammersym{p}{k}}{z^{k}}+(-1)^{n}\frac{\Pochhammersym{p}{n}e^{z}}{z^{n-1}}\genexpintE{n+p}@{z}\right)</math>]] || <code>Ei(p, z)=(exp(- z))/(z)*(sum((- 1)^(k)*(pochhammer(p, k))/((z)^(k)), k = 0..n - 1)+(- 1)^(n)*(pochhammer(p, n)*exp(z))/((z)^(n - 1))*Ei(n + p, z))</code> || <code>ExpIntegralE[p, z]=Divide[Exp[- z],z]*(Sum[(- 1)^(k)*Divide[Pochhammer[p, k],(z)^(k)], {k, 0, n - 1}]+(- 1)^(n)*Divide[Pochhammer[p, n]*Exp[z],(z)^(n - 1)]*ExpIntegralE[n + p, z])</code> || Failure || Successful || Skip || -  
 
| [https://dlmf.nist.gov/8.20.E1 8.20.E1] || [[Item:Q2714|<math>\genexpintE{p}@{z} = \frac{e^{-z}}{z}\left(\sum_{k=0}^{n-1}(-1)^{k}\frac{\Pochhammersym{p}{k}}{z^{k}}+(-1)^{n}\frac{\Pochhammersym{p}{n}e^{z}}{z^{n-1}}\genexpintE{n+p}@{z}\right)</math>]] || <code>Ei(p, z)=(exp(- z))/(z)*(sum((- 1)^(k)*(pochhammer(p, k))/((z)^(k)), k = 0..n - 1)+(- 1)^(n)*(pochhammer(p, n)*exp(z))/((z)^(n - 1))*Ei(n + p, z))</code> || <code>ExpIntegralE[p, z]=Divide[Exp[- z],z]*(Sum[(- 1)^(k)*Divide[Pochhammer[p, k],(z)^(k)], {k, 0, n - 1}]+(- 1)^(n)*Divide[Pochhammer[p, n]*Exp[z],(z)^(n - 1)]*ExpIntegralE[n + p, z])</code> || Failure || Successful || Skip || -  
 
|-
 
|-
| [https://dlmf.nist.gov/8.20.E4 8.20.E4] || [[Item:Q2717|<math>A_{k+1}(\lambda) = (1-2k\lambda)A_{k}(\lambda)+\lambda(\lambda+1)\deriv{A_{k}(\lambda)}{\lambda}</math>]] || <code>A[k + 1]*(lambda)=(1 - 2*k*lambda)* A[k]*(lambda)+ lambda*(lambda + 1)* diff(A[k]*(lambda), lambda)</code> || <code>Subscript[A, k + 1]*(\[Lambda])=(1 - 2*k*\[Lambda])* Subscript[A, k]*(\[Lambda])+ \[Lambda]*(\[Lambda]+ 1)* D[Subscript[A, k]*(\[Lambda]), \[Lambda]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-28.28427122+24.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-24.28427122+20.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-28.28427122+16.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-32.28427122+20.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br><code>20.28427123+32.28427122*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>24.28427123+28.28427122*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>20.28427123+24.28427122*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>16.28427123+28.28427122*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br><code>28.28427122-16.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>32.28427122-20.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>28.28427122-24.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>24.28427122-20.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-20.28427123-24.28427122*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-16.28427123-28.28427122*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-20.28427123-32.28427122*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-24.28427123-28.28427122*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br><code>24.28427123-28.28427122*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>20.28427123-32.28427122*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>16.28427123-28.28427122*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>20.28427123-24.28427122*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-24.28427122-20.28427123*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-28.28427122-24.28427123*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-32.28427122-20.28427123*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-28.28427122-16.28427123*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-16.28427123+28.28427122*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-20.28427123+24.28427122*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-24.28427123+28.28427122*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-20.28427123+32.28427122*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br><code>32.28427122+20.28427123*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>28.28427122+16.28427123*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>24.28427122+20.28427123*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>28.28427122+24.28427123*I <- {lambda = 2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-28.28427122+32.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-32.28427122+36.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-28.28427122+40.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-24.28427122+36.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br><code>36.28427122+24.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>32.28427122+28.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>36.28427122+32.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>40.28427122+28.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br><code>28.28427122-40.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>24.28427122-36.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>28.28427122-32.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>32.28427122-36.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-36.28427122-32.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-40.28427122-28.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-36.28427122-24.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-32.28427122-28.28427122*I <- {lambda = -2^(1/2)-I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br><code>32.28427122-28.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>36.28427122-24.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>40.28427122-28.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>36.28427122-32.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-32.28427122-36.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-28.28427122-32.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-24.28427122-36.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-28.28427122-40.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-40.28427122+28.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-36.28427122+32.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-32.28427122+28.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-36.28427122+24.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)-I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br><code>24.28427122+36.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>28.28427122+40.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>32.28427122+36.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>28.28427122+32.28427122*I <- {lambda = -2^(1/2)+I*2^(1/2), A[k] = -2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br></div></div> || Successful  
+
| [https://dlmf.nist.gov/8.20.E4 8.20.E4] || [[Item:Q2717|<math>A_{k+1}(\lambda) = (1-2k\lambda)A_{k}(\lambda)+\lambda(\lambda+1)\deriv{A_{k}(\lambda)}{\lambda}</math>]] || <code>A[k + 1]*(lambda)=(1 - 2*k*lambda)* A[k]*(lambda)+ lambda*(lambda + 1)* diff(A[k]*(lambda), lambda)</code> || <code>Subscript[A, k + 1]*(\[Lambda])=(1 - 2*k*\[Lambda])* Subscript[A, k]*(\[Lambda])+ \[Lambda]*(\[Lambda]+ 1)* D[Subscript[A, k]*(\[Lambda]), \[Lambda]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-28.28427122+24.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-24.28427122+20.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-28.28427122+16.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}</code><br><code>-32.28427122+20.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}</code><br>... skip entries to safe data<br></div></div> || Successful  
 
|-
 
|-
| [https://dlmf.nist.gov/8.21.E3 8.21.E3] || [[Item:Q2724|<math>\int_{0}^{\infty}t^{a-1}e^{+\iunit t}\diff{t} = e^{+\frac{1}{2}\pi\iunit a}\EulerGamma@{a}</math>]] || <code>int((t)^(a - 1)* exp(+ I*t), t = 0..infinity)= exp(+(1)/(2)*Pi*I*a)*GAMMA(a)</code> || <code>Integrate[(t)^(a - 1)* Exp[+ I*t], {t, 0, Infinity}]= Exp[+Divide[1,2]*Pi*I*a]*Gamma[a]</code> || Successful || Failure || - || Error
+
| [https://dlmf.nist.gov/8.21.E3 8.21.E3] || [[Item:Q2724|<math>\int_{0}^{\infty}t^{a-1}e^{+\iunit t}\diff{t} = e^{+\frac{1}{2}\pi\iunit a}\EulerGamma@{a}</math>]] || <code>int((t)^(a - 1)* exp(+ I*t), t = 0..infinity)= exp(+(1)/(2)*Pi*I*a)*GAMMA(a)</code> || <code>Integrate[(t)^(a - 1)* Exp[+ I*t], {t, 0, Infinity}]= Exp[+Divide[1,2]*Pi*I*a]*Gamma[a]</code> || Successful || Failure || - || Successful
 
|-
 
|-
| [https://dlmf.nist.gov/8.21.E3 8.21.E3] || [[Item:Q2724|<math>\int_{0}^{\infty}t^{a-1}e^{-\iunit t}\diff{t} = e^{-\frac{1}{2}\pi\iunit a}\EulerGamma@{a}</math>]] || <code>int((t)^(a - 1)* exp(- I*t), t = 0..infinity)= exp(-(1)/(2)*Pi*I*a)*GAMMA(a)</code> || <code>Integrate[(t)^(a - 1)* Exp[- I*t], {t, 0, Infinity}]= Exp[-Divide[1,2]*Pi*I*a]*Gamma[a]</code> || Successful || Failure || - || Error
+
| [https://dlmf.nist.gov/8.21.E3 8.21.E3] || [[Item:Q2724|<math>\int_{0}^{\infty}t^{a-1}e^{-\iunit t}\diff{t} = e^{-\frac{1}{2}\pi\iunit a}\EulerGamma@{a}</math>]] || <code>int((t)^(a - 1)* exp(- I*t), t = 0..infinity)= exp(-(1)/(2)*Pi*I*a)*GAMMA(a)</code> || <code>Integrate[(t)^(a - 1)* Exp[- I*t], {t, 0, Infinity}]= Exp[-Divide[1,2]*Pi*I*a]*Gamma[a]</code> || Successful || Failure || - || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/8.22.E1 8.22.E1] || [[Item:Q2750|<math>\frac{\EulerGamma@{p}}{2\pi}z^{1-p}\genexpintE{p}@{z} = \frac{\EulerGamma@{p}}{2\pi}\incGamma@{1-p}{z}</math>]] || <code>(GAMMA(p))/(2*Pi)*(z)^(1 - p)* Ei(p, z)=(GAMMA(p))/(2*Pi)*GAMMA(1 - p, z)</code> || <code>Divide[Gamma[p],2*Pi]*(z)^(1 - p)* ExpIntegralE[p, z]=Divide[Gamma[p],2*Pi]*Gamma[1 - p, z]</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/8.22.E1 8.22.E1] || [[Item:Q2750|<math>\frac{\EulerGamma@{p}}{2\pi}z^{1-p}\genexpintE{p}@{z} = \frac{\EulerGamma@{p}}{2\pi}\incGamma@{1-p}{z}</math>]] || <code>(GAMMA(p))/(2*Pi)*(z)^(1 - p)* Ei(p, z)=(GAMMA(p))/(2*Pi)*GAMMA(1 - p, z)</code> || <code>Divide[Gamma[p],2*Pi]*(z)^(1 - p)* ExpIntegralE[p, z]=Divide[Gamma[p],2*Pi]*Gamma[1 - p, z]</code> || Successful || Successful || - || -  

Latest revision as of 12:44, 19 January 2020

DLMF Formula Maple Mathematica Symbolic
Maple
Symbolic
Mathematica
Numeric
Maple
Numeric
Mathematica
8.2.E1 GAMMA(a)-GAMMA(a, z)= int((t)^(a - 1)* exp(- t), t = 0..z) Gamma[a, 0, z]= Integrate[(t)^(a - 1)* Exp[- t], {t, 0, z}] Failure Successful Skip -
8.2.E2 GAMMA(a, z)= int((t)^(a - 1)* exp(- t), t = z..infinity) Gamma[a, z]= Integrate[(t)^(a - 1)* Exp[- t], {t, z, Infinity}] Failure Failure Skip Successful
8.2.E3 GAMMA(a)-GAMMA(a, z)+ GAMMA(a, z)= GAMMA(a) Gamma[a, 0, z]+ Gamma[a, z]= Gamma[a] Successful Successful - -
8.2#Ex1 (GAMMA(a)-GAMMA(a, z))/GAMMA(a)=(GAMMA(a)-GAMMA(a, z))/(GAMMA(a)) GammaRegularized[a, 0, z]=Divide[Gamma[a, 0, z],Gamma[a]] Successful Successful - -
8.2#Ex2 GAMMA(a, z)/GAMMA(a)=(GAMMA(a, z))/(GAMMA(a)) GammaRegularized[a, z]=Divide[Gamma[a, z],Gamma[a]] Successful Successful - -
8.2.E5 (GAMMA(a)-GAMMA(a, z))/GAMMA(a)+ GAMMA(a, z)/GAMMA(a)= 1 GammaRegularized[a, 0, z]+ GammaRegularized[a, z]= 1 Successful Successful - -
8.2.E6 (z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a)= (z)^(- a)* (GAMMA(a)-GAMMA(a, z))/GAMMA(a) Error Successful Error - -
8.2.E6 (z)^(- a)* (GAMMA(a)-GAMMA(a, z))/GAMMA(a)=((z)^(- a))/(GAMMA(a))*GAMMA(a)-GAMMA(a, z) (z)^(- a)* GammaRegularized[a, 0, z]=Divide[(z)^(- a),Gamma[a]]*Gamma[a, 0, z] Failure Successful
Fail
.3504429851+.4826856014*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-.4474572306+.2704599710*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
23.62700226+82.69161801*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
3.420707652-13.57627439*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
-
8.2.E7 (z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a)=(1)/(GAMMA(a))*int((t)^(a - 1)* exp(- z*t), t = 0..1) Error Failure Error Skip -
8.2.E8 GAMMA(a)-GAMMA(a, z*exp(2*Pi*m*I))= exp(2*Pi*m*I*a)*GAMMA(a)-GAMMA(a, z) Gamma[a, 0, z*Exp[2*Pi*m*I]]= Exp[2*Pi*m*I*a]*Gamma[a, 0, z] Failure Failure Successful Successful
8.2.E9 GAMMA(a, z*exp(2*Pi*m*I))= exp(2*Pi*m*I*a)*GAMMA(a, z)+(1 - exp(2*Pi*m*I*a))* GAMMA(a) Gamma[a, z*Exp[2*Pi*m*I]]= Exp[2*Pi*m*I*a]*Gamma[a, z]+(1 - Exp[2*Pi*m*I*a])* Gamma[a] Failure Failure
Fail
-.2249049111-.4410511843e-1*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}
-.2248750758-.4411585330e-1*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}
-.2248750795-.4411584875e-1*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}
-1.005323136+.3326243216*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 1}
... skip entries to safe data
Fail
Complex[-0.22490491118791595, -0.04410511845656586] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.2248750764783257, -0.044115852492705915] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.22487507925834865, -0.04411584909968558] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.0053231382729926, 0.33262432134470665] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
8.2.E10 exp(- Pi*I*a)*GAMMA(a, z*exp(Pi*I))- exp(Pi*I*a)*GAMMA(a, z*exp(- Pi*I))= -(2*Pi*I)/(GAMMA(1 - a)) Exp[- Pi*I*a]*Gamma[a, z*Exp[Pi*I]]- Exp[Pi*I*a]*Gamma[a, z*Exp[- Pi*I]]= -Divide[2*Pi*I,Gamma[1 - a]] Failure Failure
Fail
-7167.292469-174.9289096*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
2.16987973+12.77160007*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
8.705606105-17.43270949*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-4.50134822-89.91653387*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Fail
Complex[-7167.2924809060105, -174.9289096706231] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[2.169879706441371, 12.771600034859095] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.70560609871773, -17.43270953363519] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.501348191090425, -89.91653394957189] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
8.2.E11 GAMMA(a, z*exp(+ Pi*I))= GAMMA(a)*(1 - (z)^(a)* exp(+ Pi*I*a)*(- z)^(-(a))*(GAMMA(a)-GAMMA(a, - z))/GAMMA(a)) Error Failure Error
Fail
20.46249972+81.80630504*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-1.005323138+.3326243220*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
1095.761010-111.2868863*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-1231.554386+1108.053849*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
-
8.2.E11 GAMMA(a, z*exp(- Pi*I))= GAMMA(a)*(1 - (z)^(a)* exp(- Pi*I*a)*(- z)^(-(a))*(GAMMA(a)-GAMMA(a, - z))/GAMMA(a)) Error Failure Error
Fail
1095.761010+111.2868863*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-1231.554386-1108.053849*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
20.46249972-81.80630504*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-1.005323138-.3326243220*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
... skip entries to safe data
-
8.2.E12 diff(w, [z$(2)])+(1 +(1 - a)/(z))* diff(w, z)= 0 D[w, {z, 2}]+(1 +Divide[1 - a,z])* D[w, z]= 0 Successful Successful - -
8.2.E13 diff(w, [z$(2)])-(1 +(1 - a)/(z))* diff(w, z)+(1 - a)/((z)^(2))*w = 0 D[w, {z, 2}]-(1 +Divide[1 - a,z])* D[w, z]+Divide[1 - a,(z)^(2)]*w = 0 Failure Failure
Fail
-.6464466093-.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
.6464466093+.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-.6464466093-.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
.6464466093+.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Fail
Complex[-0.6464466094067263, -0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.6464466094067263, 0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.6464466094067263, -0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.6464466094067263, 0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
8.2.E14 z*diff((+)^(-(z))*(GAMMA(z)-GAMMA(z, +))/GAMMA(z), [(a + 1 + z)*$(2)])*diff((+)^(-(z))*(GAMMA(z)-GAMMA(z, +))/GAMMA(z), a)*(0)^(-(=))*(GAMMA(=)-GAMMA(=, 0))/GAMMA(=) Error Error Error - -
8.4.E1 GAMMA((1)/(2))-GAMMA((1)/(2), (z)^(2))= 2*int(exp(- (t)^(2)), t = 0..z) Gamma[Divide[1,2], 0, (z)^(2)]= 2*Integrate[Exp[- (t)^(2)], {t, 0, z}] Failure Failure Skip
Fail
Complex[3.581461769189045, -0.9710415344467407] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[3.581461769189045, 0.9710415344467407] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
8.4.E1 2*int(exp(- (t)^(2)), t = 0..z)=sqrt(Pi)*erf(z) 2*Integrate[Exp[- (t)^(2)], {t, 0, z}]=Sqrt[Pi]*Erf[z] Successful Successful - -
8.4.E2 (0)^(-(a))*(GAMMA(a)-GAMMA(a, 0))/GAMMA(a)=(1)/(GAMMA(a + 1)) Error Failure Error
Fail
-.6493698774+1.106937485*I <- {a = 2^(1/2)+I*2^(1/2)}
-.6493698774-1.106937485*I <- {a = 2^(1/2)-I*2^(1/2)}
4.564263782+2.639434666*I <- {a = -2^(1/2)-I*2^(1/2)}
4.564263782-2.639434666*I <- {a = -2^(1/2)+I*2^(1/2)}
-
8.4.E3 (- (z)^(2))^(-((1)/(2)))*(GAMMA((1)/(2))-GAMMA((1)/(2), - (z)^(2)))/GAMMA((1)/(2))=(2*exp((z)^(2)))/(z*sqrt(Pi))*dawson(z) Error Successful Error - -
8.4.E4 GAMMA(0, z)= int((t)^(- 1)* exp(- t), t = z..infinity) Gamma[0, z]= Integrate[(t)^(- 1)* Exp[- t], {t, z, Infinity}] Successful Failure - Successful
8.4.E4 int((t)^(- 1)* exp(- t), t = z..infinity)= Ei(z) Integrate[(t)^(- 1)* Exp[- t], {t, z, Infinity}]= -ExpIntegralEi[-(z)] Failure Failure Skip Successful
8.4.E5 GAMMA(1, z)= exp(- z) Gamma[1, z]= Exp[- z] Successful Successful - -
8.4.E6 GAMMA((1)/(2), (z)^(2))= 2*int(exp(- (t)^(2)), t = z..infinity) Gamma[Divide[1,2], (z)^(2)]= 2*Integrate[Exp[- (t)^(2)], {t, z, Infinity}] Failure Failure Skip
Fail
Complex[-3.581461769189044, 0.9710415344467407] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.581461769189044, -0.9710415344467407] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
8.4.E6 2*int(exp(- (t)^(2)), t = z..infinity)=sqrt(Pi)*erfc(z) 2*Integrate[Exp[- (t)^(2)], {t, z, Infinity}]=Sqrt[Pi]*Erfc[z] Successful Successful - -
8.4.E7 GAMMA(n + 1)-GAMMA(n + 1, z)= factorial(n)*(1 - exp(- z)*exp(1)[n]*(z)) Gamma[n + 1, 0, z]= (n)!*(1 - Exp[- z]*Subscript[E, n]*(z)) Failure Failure Error Successful
8.4.E8 GAMMA(n + 1, z)= factorial(n)*exp(- z)*exp(1)[n]*(z) Gamma[n + 1, z]= (n)!*Exp[- z]*Subscript[E, n]*(z) Failure Failure Error Successful
8.4.E9 (GAMMA(n + 1)-GAMMA(n + 1, z))/GAMMA(n + 1)= 1 - exp(- z)*exp(1)[n]*(z) GammaRegularized[n + 1, 0, z]= 1 - Exp[- z]*Subscript[E, n]*(z) Failure Failure Error Successful
8.4.E10 GAMMA(n + 1, z)/GAMMA(n + 1)= exp(- z)*exp(1)[n]*(z) GammaRegularized[n + 1, z]= Exp[- z]*Subscript[E, n]*(z) Failure Failure Error Successful
8.4.E12 (z)^(-(- n))*(GAMMA(- n)-GAMMA(- n, z))/GAMMA(- n)= (z)^(n) Error Failure Error
Fail
Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)+I*2^(1/2), n = 1}
Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)+I*2^(1/2), n = 2}
Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)+I*2^(1/2), n = 3}
Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)-I*2^(1/2), n = 1}
... skip entries to safe data
-
8.4.E13 GAMMA(1 - n, z)= (z)^(1 - n)* Ei(n, z) Gamma[1 - n, z]= (z)^(1 - n)* ExpIntegralE[n, z] Successful Successful - -
8.4.E14 GAMMA(n +(1)/(2), (z)^(2))/GAMMA(n +(1)/(2))= erfc(z)+(exp(- (z)^(2)))/(sqrt(Pi))*sum(((z)^(2*k - 1))/(pochhammer((1)/(2), k)), k = 1..n) GammaRegularized[n +Divide[1,2], (z)^(2)]= Erfc[z]+Divide[Exp[- (z)^(2)],Sqrt[Pi]]*Sum[Divide[(z)^(2*k - 1),Pochhammer[Divide[1,2], k]], {k, 1, n}] Failure Failure Skip
Fail
Complex[-6.522116143801526, 0.8770870118427658] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-7.400077458243353, -11.126893574158686] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[11.80629147935897, -12.531631677265604] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.522116143801526, -0.8770870118427658] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
8.4.E15 GAMMA(- n, z)=((- 1)^(n))/(factorial(n))*(Ei(z)- exp(- z)*sum(((- 1)^(k)* factorial(k))/((z)^(k + 1)), k = 0..n - 1)) Gamma[- n, z]=Divide[(- 1)^(n),(n)!]*(-ExpIntegralEi[-(z)]- Exp[- z]*Sum[Divide[(- 1)^(k)* (k)!,(z)^(k + 1)], {k, 0, n - 1}]) Failure Failure Skip
Fail
Complex[1.3877787807814457*^-17, 3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.734723475976807*^-18, -1.5707963267948966] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.3368086899420177*^-19, 0.5235987755982987] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.3877787807814457*^-17, -3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
8.5.E1 GAMMA(a)-GAMMA(a, z)= (a)^(- 1)* (z)^(a)* exp(- z)*KummerM(1, 1 + a, z) Gamma[a, 0, z]= (a)^(- 1)* (z)^(a)* Exp[- z]*Hypergeometric1F1[1, 1 + a, z] Successful Successful - -
8.5.E1 (a)^(- 1)* (z)^(a)* exp(- z)*KummerM(1, 1 + a, z)= (a)^(- 1)* (z)^(a)* KummerM(a, 1 + a, - z) (a)^(- 1)* (z)^(a)* Exp[- z]*Hypergeometric1F1[1, 1 + a, z]= (a)^(- 1)* (z)^(a)* Hypergeometric1F1[a, 1 + a, - z] Successful Successful - -
8.5.E2 (z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a)= exp(- z)*KummerM(1, 1 + a, z)/GAMMA(1 + a) Error Successful Error - -
8.5.E2 exp(- z)*KummerM(1, 1 + a, z)/GAMMA(1 + a)= KummerM(a, 1 + a, - z)/GAMMA(1 + a) Exp[- z]*Hypergeometric1F1Regularized[1, 1 + a, z]= Hypergeometric1F1Regularized[a, 1 + a, - z] Successful Successful - -
8.5.E3 GAMMA(a, z)= exp(- z)*KummerU(1 - a, 1 - a, z) Gamma[a, z]= Exp[- z]*HypergeometricU[1 - a, 1 - a, z] Successful Successful - -
8.5.E3 exp(- z)*KummerU(1 - a, 1 - a, z)= (z)^(a)* exp(- z)*KummerU(1, 1 + a, z) Exp[- z]*HypergeometricU[1 - a, 1 - a, z]= (z)^(a)* Exp[- z]*HypergeometricU[1, 1 + a, z] Successful Successful - -
8.5.E4 GAMMA(a)-GAMMA(a, z)= (a)^(- 1)* (z)^((1)/(2)*a -(1)/(2))* exp(-(1)/(2)*z)*WhittakerM((1)/(2)*a -(1)/(2), (1)/(2)*a, z) Gamma[a, 0, z]= (a)^(- 1)* (z)^(Divide[1,2]*a -Divide[1,2])* Exp[-Divide[1,2]*z]*WhittakerM[Divide[1,2]*a -Divide[1,2], Divide[1,2]*a, z] Successful Successful - -
8.5.E5 GAMMA(a, z)= exp(-(1)/(2)*z)*(z)^((1)/(2)*a -(1)/(2))* WhittakerW((1)/(2)*a -(1)/(2), (1)/(2)*a, z) Gamma[a, z]= Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]*a -Divide[1,2])* WhittakerW[Divide[1,2]*a -Divide[1,2], Divide[1,2]*a, z] Successful Successful - -
8.6.E1 GAMMA(a)-GAMMA(a, z)=((z)^(a))/(sin(Pi*a))*int(exp(z*cos(t))*cos(a*t + z*sin(t)), t = 0..Pi) Gamma[a, 0, z]=Divide[(z)^(a),Sin[Pi*a]]*Integrate[Exp[z*Cos[t]]*Cos[a*t + z*Sin[t]], {t, 0, Pi}] Failure Failure Skip Error
8.6.E2 GAMMA(a)-GAMMA(a, z)= (z)^((1)/(2)*a)* int(exp(- t)*(t)^((1)/(2)*a - 1)* BesselJ(a, 2*sqrt(z*t)), t = 0..infinity) Gamma[a, 0, z]= (z)^(Divide[1,2]*a)* Integrate[Exp[- t]*(t)^(Divide[1,2]*a - 1)* BesselJ[a, 2*Sqrt[z*t]], {t, 0, Infinity}] Failure Failure Skip Error
8.6.E3 GAMMA(a)-GAMMA(a, z)= (z)^(a)* int(exp(- a*t - z*exp(- t)), t = 0..infinity) Gamma[a, 0, z]= (z)^(a)* Integrate[Exp[- a*t - z*Exp[- t]], {t, 0, Infinity}] Failure Failure Skip Successful
8.6.E4 GAMMA(a, z)=((z)^(a)* exp(- z))/(GAMMA(1 - a))*int(((t)^(- a)* exp(- t))/(z + t), t = 0..infinity) Gamma[a, z]=Divide[(z)^(a)* Exp[- z],Gamma[1 - a]]*Integrate[Divide[(t)^(- a)* Exp[- t],z + t], {t, 0, Infinity}] Failure Failure Skip Successful
8.6.E5 GAMMA(a, z)= (z)^(a)* exp(- z)*int((exp(- z*t))/((1 + t)^(1 - a)), t = 0..infinity) Gamma[a, z]= (z)^(a)* Exp[- z]*Integrate[Divide[Exp[- z*t],(1 + t)^(1 - a)], {t, 0, Infinity}] Successful Failure - Error
8.6.E6 GAMMA(a, z)=(2*(z)^((1)/(2)*a)* exp(- z))/(GAMMA(1 - a))*int(exp(- t)*(t)^(-(1)/(2)*a)* BesselK(a, 2*sqrt(z*t)), t = 0..infinity) Gamma[a, z]=Divide[2*(z)^(Divide[1,2]*a)* Exp[- z],Gamma[1 - a]]*Integrate[Exp[- t]*(t)^(-Divide[1,2]*a)* BesselK[a, 2*Sqrt[z*t]], {t, 0, Infinity}] Successful Failure - Error
8.6.E7 GAMMA(a, z)= (z)^(a)* int(exp(a*t - z*exp(t)), t = 0..infinity) Gamma[a, z]= (z)^(a)* Integrate[Exp[a*t - z*Exp[t]], {t, 0, Infinity}] Failure Failure Skip Error
8.6.E8 GAMMA(a)-GAMMA(a, z)=(- I*(z)^(a))/(2*sin(Pi*a))*int((t)^(a - 1)* exp(z*t), t = - 1..(0 +)) Gamma[a, 0, z]=Divide[- I*(z)^(a),2*Sin[Pi*a]]*Integrate[(t)^(a - 1)* Exp[z*t], {t, - 1, (0 +)}] Error Failure - Error
8.6.E9 GAMMA(- a, z*exp(+ Pi*I))=(exp(z)*exp(- Pi*I*a))/(GAMMA(1 + a))*int(((t)^(a)* exp(- z*t))/(t - 1), t = 0..infinity) Gamma[- a, z*Exp[+ Pi*I]]=Divide[Exp[z]*Exp[- Pi*I*a],Gamma[1 + a]]*Integrate[Divide[(t)^(a)* Exp[- z*t],t - 1], {t, 0, Infinity}] Failure Failure Skip Error
8.6.E9 GAMMA(- a, z*exp(- Pi*I))=(exp(z)*exp(+ Pi*I*a))/(GAMMA(1 + a))*int(((t)^(a)* exp(- z*t))/(t - 1), t = 0..infinity) Gamma[- a, z*Exp[- Pi*I]]=Divide[Exp[z]*Exp[+ Pi*I*a],Gamma[1 + a]]*Integrate[Divide[(t)^(a)* Exp[- z*t],t - 1], {t, 0, Infinity}] Failure Failure Skip Error
8.6.E10 GAMMA(a)-GAMMA(a, z)=(1)/(2*Pi*I)*int((GAMMA(s))/(a - s)*(z)^(a - s), s = c - I*infinity..c + I*infinity) Gamma[a, 0, z]=Divide[1,2*Pi*I]*Integrate[Divide[Gamma[s],a - s]*(z)^(a - s), {s, c - I*Infinity, c + I*Infinity}] Failure Failure Skip Error
8.6.E11 GAMMA(a, z)=(1)/(2*Pi*I)*int(GAMMA(s + a)*((z)^(- s))/(s), s = c - I*infinity..c + I*infinity) Gamma[a, z]=Divide[1,2*Pi*I]*Integrate[Gamma[s + a]*Divide[(z)^(- s),s], {s, c - I*Infinity, c + I*Infinity}] Failure Failure Skip Error
8.6.E12 GAMMA(a, z)= -((z)^(a - 1)* exp(- z))/(GAMMA(1 - a))*(1)/(2*Pi*I)*int(GAMMA(s + 1 - a)*(Pi*(z)^(- s))/(sin(Pi*s)), s = c - I*infinity..c + I*infinity) Gamma[a, z]= -Divide[(z)^(a - 1)* Exp[- z],Gamma[1 - a]]*Divide[1,2*Pi*I]*Integrate[Gamma[s + 1 - a]*Divide[Pi*(z)^(- s),Sin[Pi*s]], {s, c - I*Infinity, c + I*Infinity}] Failure Failure Skip Error
8.7.E1 (z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a)= exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..infinity) Error Successful Error - -
8.7.E1 exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..infinity)=(1)/(GAMMA(a))*sum(((- z)^(k))/(factorial(k)*(a + k)), k = 0..infinity) Exp[- z]*Sum[Divide[(z)^(k),Gamma[a + k + 1]], {k, 0, Infinity}]=Divide[1,Gamma[a]]*Sum[Divide[(- z)^(k),(k)!*(a + k)], {k, 0, Infinity}] Successful Successful - -
8.7.E3 GAMMA(a, z)= GAMMA(a)- sum(((- 1)^(k)* (z)^(a + k))/(factorial(k)*(a + k)), k = 0..infinity) Gamma[a, z]= Gamma[a]- Sum[Divide[(- 1)^(k)* (z)^(a + k),(k)!*(a + k)], {k, 0, Infinity}] Successful Successful - -
8.7.E3 GAMMA(a)- sum(((- 1)^(k)* (z)^(a + k))/(factorial(k)*(a + k)), k = 0..infinity)= GAMMA(a)*(1 - (z)^(a)* exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..infinity)) Gamma[a]- Sum[Divide[(- 1)^(k)* (z)^(a + k),(k)!*(a + k)], {k, 0, Infinity}]= Gamma[a]*(1 - (z)^(a)* Exp[- z]*Sum[Divide[(z)^(k),Gamma[a + k + 1]], {k, 0, Infinity}]) Successful Successful - -
8.8.E1 GAMMA(a + 1)-GAMMA(a + 1, z)= a*GAMMA(a)-GAMMA(a, z)- (z)^(a)* exp(- z) Gamma[a + 1, 0, z]= a*Gamma[a, 0, z]- (z)^(a)* Exp[- z] Failure Successful
Fail
.135004907e-1-.2375774782*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
.8693672828+.710002389*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
107.1902160-63.3824277*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-.1657436948-.7422690683*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
-
8.8.E2 GAMMA(a + 1, z)= a*GAMMA(a, z)+ (z)^(a)* exp(- z) Gamma[a + 1, z]= a*Gamma[a, z]+ (z)^(a)* Exp[- z] Failure Successful Successful -
8.8.E4 z*(z)^(-(a + 1))*(GAMMA(a + 1)-GAMMA(a + 1, z))/GAMMA(a + 1)= (z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a)-(exp(- z))/(GAMMA(a + 1)) Error Failure Error Successful -
8.8.E5 (GAMMA(a + 1)-GAMMA(a + 1, z))/GAMMA(a + 1)= (GAMMA(a)-GAMMA(a, z))/GAMMA(a)-((z)^(a)* exp(- z))/(GAMMA(a + 1)) GammaRegularized[a + 1, 0, z]= GammaRegularized[a, 0, z]-Divide[(z)^(a)* Exp[- z],Gamma[a + 1]] Failure Successful Successful -
8.8.E6 GAMMA(a + 1, z)/GAMMA(a + 1)= GAMMA(a, z)/GAMMA(a)+((z)^(a)* exp(- z))/(GAMMA(a + 1)) GammaRegularized[a + 1, z]= GammaRegularized[a, z]+Divide[(z)^(a)* Exp[- z],Gamma[a + 1]] Failure Successful Successful -
8.8.E7 GAMMA(a + n)-GAMMA(a + n, z)= pochhammer(a, n)*GAMMA(a)-GAMMA(a, z)- (z)^(a)* exp(- z)*sum((GAMMA(a + n))/(GAMMA(a + k + 1))*(z)^(k), k = 0..n - 1) Gamma[a + n, 0, z]= Pochhammer[a, n]*Gamma[a, 0, z]- (z)^(a)* Exp[- z]*Sum[Divide[Gamma[a + n],Gamma[a + k + 1]]*(z)^(k), {k, 0, n - 1}] Failure Successful Skip -
8.8.E8 GAMMA(a)-GAMMA(a, z)=(GAMMA(a))/(GAMMA(a - n))*GAMMA(a - n)-GAMMA(a - n, z)- (z)^(a - 1)* exp(- z)*sum((GAMMA(a))/(GAMMA(a - k))*(z)^(- k), k = 0..n - 1) Gamma[a, 0, z]=Divide[Gamma[a],Gamma[a - n]]*Gamma[a - n, 0, z]- (z)^(a - 1)* Exp[- z]*Sum[Divide[Gamma[a],Gamma[a - k]]*(z)^(- k), {k, 0, n - 1}] Failure Successful Skip -
8.8.E9 GAMMA(a + n, z)= pochhammer(a, n)*GAMMA(a, z)+ (z)^(a)* exp(- z)*sum((GAMMA(a + n))/(GAMMA(a + k + 1))*(z)^(k), k = 0..n - 1) Gamma[a + n, z]= Pochhammer[a, n]*Gamma[a, z]+ (z)^(a)* Exp[- z]*Sum[Divide[Gamma[a + n],Gamma[a + k + 1]]*(z)^(k), {k, 0, n - 1}] Successful Successful - -
8.8.E10 GAMMA(a, z)=(GAMMA(a))/(GAMMA(a - n))*GAMMA(a - n, z)+ (z)^(a - 1)* exp(- z)*sum((GAMMA(a))/(GAMMA(a - k))*(z)^(- k), k = 0..n - 1) Gamma[a, z]=Divide[Gamma[a],Gamma[a - n]]*Gamma[a - n, z]+ (z)^(a - 1)* Exp[- z]*Sum[Divide[Gamma[a],Gamma[a - k]]*(z)^(- k), {k, 0, n - 1}] Failure Successful Skip -
8.8.E11 (GAMMA(a + n)-GAMMA(a + n, z))/GAMMA(a + n)= (GAMMA(a)-GAMMA(a, z))/GAMMA(a)- (z)^(a)* exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..n - 1) GammaRegularized[a + n, 0, z]= GammaRegularized[a, 0, z]- (z)^(a)* Exp[- z]*Sum[Divide[(z)^(k),Gamma[a + k + 1]], {k, 0, n - 1}] Successful Successful - -
8.8.E12