Difference between revisions of "Results of Error Functions, Dawson’s and Fresnel Integrals"

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| [https://dlmf.nist.gov/7.5.E6 7.5.E6] || [[Item:Q2352|<math>e^{-\frac{1}{2}\pi iz^{2}}(\auxFresnelg@{z}- i\auxFresnelf@{z}) = \tfrac{1}{2}(1- i)-(\Fresnelcosint@{z}- i\Fresnelsinint@{z})</math>]] || <code>exp(-(1)/(2)*Pi*I*(z)^(2))*(Fresnelg(z)- I*Fresnelf(z))=(1)/(2)*(1 - I)-(FresnelC(z)- I*FresnelS(z))</code> || <code>Exp[-Divide[1,2]*Pi*I*(z)^(2)]*(FresnelG[z]- I*FresnelF[z])=Divide[1,2]*(1 - I)-(FresnelC[z]- I*FresnelS[z])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.149314e-2+.173022e-2*I <- {z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.119473e-2-.149314e-2*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br></div></div> || Successful  
 
| [https://dlmf.nist.gov/7.5.E6 7.5.E6] || [[Item:Q2352|<math>e^{-\frac{1}{2}\pi iz^{2}}(\auxFresnelg@{z}- i\auxFresnelf@{z}) = \tfrac{1}{2}(1- i)-(\Fresnelcosint@{z}- i\Fresnelsinint@{z})</math>]] || <code>exp(-(1)/(2)*Pi*I*(z)^(2))*(Fresnelg(z)- I*Fresnelf(z))=(1)/(2)*(1 - I)-(FresnelC(z)- I*FresnelS(z))</code> || <code>Exp[-Divide[1,2]*Pi*I*(z)^(2)]*(FresnelG[z]- I*FresnelF[z])=Divide[1,2]*(1 - I)-(FresnelC[z]- I*FresnelS[z])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.149314e-2+.173022e-2*I <- {z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.119473e-2-.149314e-2*I <- {z = -2^(1/2)-I*2^(1/2)}</code><br></div></div> || Successful  
 
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| [https://dlmf.nist.gov/7.5.E8 7.5.E8] || [[Item:Q2354|<math>\Fresnelcosint@{z}+ i\Fresnelsinint@{z} = \tfrac{1}{2}(1+ i)\erf@@{\zeta}</math>]] || <code>FresnelC(z)+ I*FresnelS(z)=(1)/(2)*(1 + I)* erf(zeta)</code> || <code>FresnelC[z]+ I*FresnelS[z]=Divide[1,2]*(1 + I)* Erf[\[zeta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.1423151062+.1316106532*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>.1316106532-.1423151062*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>1.141922366+.8679966068*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>.8679966068+1.141922366*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br><code>66.52540791-67.53571963*I <- {z = 2^(1/2)-I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>66.79933367-67.80964539*I <- {z = 2^(1/2)-I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>67.80964539-66.79933367*I <- {z = 2^(1/2)-I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>67.53571963-66.52540791*I <- {z = 2^(1/2)-I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br><code>-1.141922366-.8679966068*I <- {z = -2^(1/2)-I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>-.8679966068-1.141922366*I <- {z = -2^(1/2)-I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>.1423151062-.1316106532*I <- {z = -2^(1/2)-I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>-.1316106532+.1423151062*I <- {z = -2^(1/2)-I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br><code>-67.80964539+66.79933367*I <- {z = -2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>-67.53571963+66.52540791*I <- {z = -2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>-66.52540791+67.53571963*I <- {z = -2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>-66.79933367+67.80964539*I <- {z = -2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || Error  
+
| [https://dlmf.nist.gov/7.5.E8 7.5.E8] || [[Item:Q2354|<math>\Fresnelcosint@{z}+ i\Fresnelsinint@{z} = \tfrac{1}{2}(1+ i)\erf@@{\zeta}</math>]] || <code>FresnelC(z)+ I*FresnelS(z)=(1)/(2)*(1 + I)* erf(zeta)</code> || <code>FresnelC[z]+ I*FresnelS[z]=Divide[1,2]*(1 + I)* Erf[\[zeta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.1423151062+.1316106532*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>.1316106532-.1423151062*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>1.141922366+.8679966068*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>.8679966068+1.141922366*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Error  
 
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| [https://dlmf.nist.gov/7.5.E8 7.5.E8] || [[Item:Q2354|<math>\Fresnelcosint@{z}- i\Fresnelsinint@{z} = \tfrac{1}{2}(1- i)\erf@@{\zeta}</math>]] || <code>FresnelC(z)- I*FresnelS(z)=(1)/(2)*(1 - I)* erf(zeta)</code> || <code>FresnelC[z]- I*FresnelS[z]=Divide[1,2]*(1 - I)* Erf[\[zeta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>66.79933367+67.80964539*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>66.52540791+67.53571963*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>67.53571963+66.52540791*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>67.80964539+66.79933367*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br><code>.1316106532+.1423151062*I <- {z = 2^(1/2)-I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>-.1423151062-.1316106532*I <- {z = 2^(1/2)-I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>.8679966068-1.141922366*I <- {z = 2^(1/2)-I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>1.141922366-.8679966068*I <- {z = 2^(1/2)-I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br><code>-67.53571963-66.52540791*I <- {z = -2^(1/2)-I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>-67.80964539-66.79933367*I <- {z = -2^(1/2)-I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>-66.79933367-67.80964539*I <- {z = -2^(1/2)-I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>-66.52540791-67.53571963*I <- {z = -2^(1/2)-I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br><code>-.8679966068+1.141922366*I <- {z = -2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.141922366+.8679966068*I <- {z = -2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>-.1316106532-.1423151062*I <- {z = -2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>.1423151062+.1316106532*I <- {z = -2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || Error  
+
| [https://dlmf.nist.gov/7.5.E8 7.5.E8] || [[Item:Q2354|<math>\Fresnelcosint@{z}- i\Fresnelsinint@{z} = \tfrac{1}{2}(1- i)\erf@@{\zeta}</math>]] || <code>FresnelC(z)- I*FresnelS(z)=(1)/(2)*(1 - I)* erf(zeta)</code> || <code>FresnelC[z]- I*FresnelS[z]=Divide[1,2]*(1 - I)* Erf[\[zeta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>66.79933367+67.80964539*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>66.52540791+67.53571963*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>67.53571963+66.52540791*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>67.80964539+66.79933367*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Error  
 
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| [https://dlmf.nist.gov/7.5.E10 7.5.E10] || [[Item:Q2356|<math>\auxFresnelg@{z}+ i\auxFresnelf@{z} = \tfrac{1}{2}(1+ i)e^{\zeta^{2}}\erfc@@{\zeta}</math>]] || <code>Fresnelg(z)+ I*Fresnelf(z)=(1)/(2)*(1 + I)* exp((zeta)^(2))*erfc(zeta)</code> || <code>FresnelG[z]+ I*FresnelF[z]=Divide[1,2]*(1 + I)* Exp[(\[zeta])^(2)]*Erfc[\[zeta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.874918896e-1+.8375300635e-1*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>.8375400635e-1-.874928896e-1*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>.1946430180+1.537001110*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>1.537002110+.1946420180*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br><code>-.3171418896+.1049610064*I <- {z = 2^(1/2)-I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>-.1458959936-.662848896e-1*I <- {z = 2^(1/2)-I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>-.3500698200e-1+1.558209110*I <- {z = 2^(1/2)-I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>1.307352110+.2158500180*I <- {z = 2^(1/2)-I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br><code>535.1938521+535.3651000*I <- {z = -2^(1/2)-I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>535.3650980+535.1938541*I <- {z = -2^(1/2)-I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>535.4759870+536.8183481*I <- {z = -2^(1/2)-I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>536.8183461+535.4759890*I <- {z = -2^(1/2)-I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br><code>-.662838896e-1-.1458959936*I <- {z = -2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>.1049620064-.3171418896*I <- {z = -2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>.2158510180+1.307352110*I <- {z = -2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>1.558210110-.3500698200e-1*I <- {z = -2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || Error  
+
| [https://dlmf.nist.gov/7.5.E10 7.5.E10] || [[Item:Q2356|<math>\auxFresnelg@{z}+ i\auxFresnelf@{z} = \tfrac{1}{2}(1+ i)e^{\zeta^{2}}\erfc@@{\zeta}</math>]] || <code>Fresnelg(z)+ I*Fresnelf(z)=(1)/(2)*(1 + I)* exp((zeta)^(2))*erfc(zeta)</code> || <code>FresnelG[z]+ I*FresnelF[z]=Divide[1,2]*(1 + I)* Exp[(\[zeta])^(2)]*Erfc[\[zeta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.874918896e-1+.8375300635e-1*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>.8375400635e-1-.874928896e-1*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>.1946430180+1.537001110*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>1.537002110+.1946420180*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Error  
 
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| [https://dlmf.nist.gov/7.5.E10 7.5.E10] || [[Item:Q2356|<math>\auxFresnelg@{z}- i\auxFresnelf@{z} = \tfrac{1}{2}(1- i)e^{\zeta^{2}}\erfc@@{\zeta}</math>]] || <code>Fresnelg(z)- I*Fresnelf(z)=(1)/(2)*(1 - I)* exp((zeta)^(2))*erfc(zeta)</code> || <code>FresnelG[z]- I*FresnelF[z]=Divide[1,2]*(1 - I)* Exp[(\[zeta])^(2)]*Erfc[\[zeta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.1458959936+.662848896e-1*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>-.3171418896-.1049610064*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>1.307352110-.2158500180*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>-.3500698200e-1-1.558209110*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br><code>.8375400635e-1+.874928896e-1*I <- {z = 2^(1/2)-I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>-.874918896e-1-.8375300635e-1*I <- {z = 2^(1/2)-I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>1.537002110-.1946420180*I <- {z = 2^(1/2)-I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>.1946430180-1.537001110*I <- {z = 2^(1/2)-I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br><code>.1049620064+.3171418896*I <- {z = -2^(1/2)-I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>-.662838896e-1+.1458959936*I <- {z = -2^(1/2)-I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>1.558210110+.3500698200e-1*I <- {z = -2^(1/2)-I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>.2158510180-1.307352110*I <- {z = -2^(1/2)-I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br><code>535.3650980-535.1938541*I <- {z = -2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>535.1938521-535.3651000*I <- {z = -2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>536.8183461-535.4759890*I <- {z = -2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>535.4759870-536.8183481*I <- {z = -2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || Error  
+
| [https://dlmf.nist.gov/7.5.E10 7.5.E10] || [[Item:Q2356|<math>\auxFresnelg@{z}- i\auxFresnelf@{z} = \tfrac{1}{2}(1- i)e^{\zeta^{2}}\erfc@@{\zeta}</math>]] || <code>Fresnelg(z)- I*Fresnelf(z)=(1)/(2)*(1 - I)* exp((zeta)^(2))*erfc(zeta)</code> || <code>FresnelG[z]- I*FresnelF[z]=Divide[1,2]*(1 - I)* Exp[(\[zeta])^(2)]*Erfc[\[zeta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.1458959936+.662848896e-1*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>-.3171418896-.1049610064*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>1.307352110-.2158500180*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>-.3500698200e-1-1.558209110*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Error  
 
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| [https://dlmf.nist.gov/7.6.E1 7.6.E1] || [[Item:Q2360|<math>\erf@@{z} = \frac{2}{\sqrt{\pi}}\sum_{n=0}^{\infty}\frac{(-1)^{n}z^{2n+1}}{n!(2n+1)}</math>]] || <code>erf(z)=(2)/(sqrt(Pi))*sum(((- 1)^(n)* (z)^(2*n + 1))/(factorial(n)*(2*n + 1)), n = 0..infinity)</code> || <code>Erf[z]=Divide[2,Sqrt[Pi]]*Sum[Divide[(- 1)^(n)* (z)^(2*n + 1),(n)!*(2*n + 1)], {n, 0, Infinity}]</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/7.6.E1 7.6.E1] || [[Item:Q2360|<math>\erf@@{z} = \frac{2}{\sqrt{\pi}}\sum_{n=0}^{\infty}\frac{(-1)^{n}z^{2n+1}}{n!(2n+1)}</math>]] || <code>erf(z)=(2)/(sqrt(Pi))*sum(((- 1)^(n)* (z)^(2*n + 1))/(factorial(n)*(2*n + 1)), n = 0..infinity)</code> || <code>Erf[z]=Divide[2,Sqrt[Pi]]*Sum[Divide[(- 1)^(n)* (z)^(2*n + 1),(n)!*(2*n + 1)], {n, 0, Infinity}]</code> || Successful || Successful || - || -  
Line 83: Line 83:
 
| [https://dlmf.nist.gov/7.7.E1 7.7.E1] || [[Item:Q2371|<math>\erfc@@{z} = \frac{2}{\pi}e^{-z^{2}}\int_{0}^{\infty}\frac{e^{-z^{2}t^{2}}}{t^{2}+1}\diff{t}</math>]] || <code>erfc(z)=(2)/(Pi)*exp(- (z)^(2))*int((exp(- (z)^(2)* (t)^(2)))/((t)^(2)+ 1), t = 0..infinity)</code> || <code>Erfc[z]=Divide[2,Pi]*Exp[- (z)^(2)]*Integrate[Divide[Exp[- (z)^(2)* (t)^(2)],(t)^(2)+ 1], {t, 0, Infinity}]</code> || Successful || Failure || - || Error  
 
| [https://dlmf.nist.gov/7.7.E1 7.7.E1] || [[Item:Q2371|<math>\erfc@@{z} = \frac{2}{\pi}e^{-z^{2}}\int_{0}^{\infty}\frac{e^{-z^{2}t^{2}}}{t^{2}+1}\diff{t}</math>]] || <code>erfc(z)=(2)/(Pi)*exp(- (z)^(2))*int((exp(- (z)^(2)* (t)^(2)))/((t)^(2)+ 1), t = 0..infinity)</code> || <code>Erfc[z]=Divide[2,Pi]*Exp[- (z)^(2)]*Integrate[Divide[Exp[- (z)^(2)* (t)^(2)],(t)^(2)+ 1], {t, 0, Infinity}]</code> || Successful || Failure || - || Error  
 
|-
 
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| [https://dlmf.nist.gov/7.7.E2 7.7.E2] || [[Item:Q2372|<math>\frac{1}{\pi i}\int_{-\infty}^{\infty}\frac{e^{-t^{2}}\diff{t}}{t-z} = \frac{2z}{\pi i}\int_{0}^{\infty}\frac{e^{-t^{2}}\diff{t}}{t^{2}-z^{2}}</math>]] || <code>(1)/(Pi*I)*int((exp(- (t)^(2)))/(t - z), t = - infinity..infinity)=(2*z)/(Pi*I)*int((exp(- (t)^(2)))/((t)^(2)- (z)^(2)), t = 0..infinity)</code> || <code>Divide[1,Pi*I]*Integrate[Divide[Exp[- (t)^(2)],t - z], {t, - Infinity, Infinity}]=Divide[2*z,Pi*I]*Integrate[Divide[Exp[- (t)^(2)],(t)^(2)- (z)^(2)], {t, 0, Infinity}]</code> || Failure || Failure || Skip || Skip
+
| [https://dlmf.nist.gov/7.7.E2 7.7.E2] || [[Item:Q2372|<math>\frac{1}{\pi i}\int_{-\infty}^{\infty}\frac{e^{-t^{2}}\diff{t}}{t-z} = \frac{2z}{\pi i}\int_{0}^{\infty}\frac{e^{-t^{2}}\diff{t}}{t^{2}-z^{2}}</math>]] || <code>(1)/(Pi*I)*int((exp(- (t)^(2)))/(t - z), t = - infinity..infinity)=(2*z)/(Pi*I)*int((exp(- (t)^(2)))/((t)^(2)- (z)^(2)), t = 0..infinity)</code> || <code>Divide[1,Pi*I]*Integrate[Divide[Exp[- (t)^(2)],t - z], {t, - Infinity, Infinity}]=Divide[2*z,Pi*I]*Integrate[Divide[Exp[- (t)^(2)],(t)^(2)- (z)^(2)], {t, 0, Infinity}]</code> || Failure || Failure || Skip || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/7.7.E3 7.7.E3] || [[Item:Q2373|<math>\int_{0}^{\infty}e^{-at^{2}+2izt}\diff{t} = \frac{1}{2}\sqrt{\frac{\pi}{a}}e^{-z^{2}/a}+\frac{i}{\sqrt{a}}\DawsonsintF@{\frac{z}{\sqrt{a}}}</math>]] || <code>int(exp(- a*(t)^(2)+ 2*I*z*t), t = 0..infinity)=(1)/(2)*sqrt((Pi)/(a))*exp(- (z)^(2)/ a)+(I)/(sqrt(a))*dawson((z)/(sqrt(a)))</code> || <code>Integrate[Exp[- a*(t)^(2)+ 2*I*z*t], {t, 0, Infinity}]=Divide[1,2]*Sqrt[Divide[Pi,a]]*Exp[- (z)^(2)/ a]+Divide[I,Sqrt[a]]*DawsonF[Divide[z,Sqrt[a]]]</code> || Failure || Successful || Skip || -  
 
| [https://dlmf.nist.gov/7.7.E3 7.7.E3] || [[Item:Q2373|<math>\int_{0}^{\infty}e^{-at^{2}+2izt}\diff{t} = \frac{1}{2}\sqrt{\frac{\pi}{a}}e^{-z^{2}/a}+\frac{i}{\sqrt{a}}\DawsonsintF@{\frac{z}{\sqrt{a}}}</math>]] || <code>int(exp(- a*(t)^(2)+ 2*I*z*t), t = 0..infinity)=(1)/(2)*sqrt((Pi)/(a))*exp(- (z)^(2)/ a)+(I)/(sqrt(a))*dawson((z)/(sqrt(a)))</code> || <code>Integrate[Exp[- a*(t)^(2)+ 2*I*z*t], {t, 0, Infinity}]=Divide[1,2]*Sqrt[Divide[Pi,a]]*Exp[- (z)^(2)/ a]+Divide[I,Sqrt[a]]*DawsonF[Divide[z,Sqrt[a]]]</code> || Failure || Successful || Skip || -  
 
|-
 
|-
| [https://dlmf.nist.gov/7.7.E4 7.7.E4] || [[Item:Q2374|<math>\int_{0}^{\infty}\frac{e^{-at}}{\sqrt{t+z^{2}}}\diff{t} = \sqrt{\frac{\pi}{a}}e^{az^{2}}\erfc@{\sqrt{a}z}</math>]] || <code>int((exp(- a*t))/(sqrt(t + (z)^(2))), t = 0..infinity)=sqrt((Pi)/(a))*exp(a*(z)^(2))*erfc(sqrt(a)*z)</code> || <code>Integrate[Divide[Exp[- a*t],Sqrt[t + (z)^(2)]], {t, 0, Infinity}]=Sqrt[Divide[Pi,a]]*Exp[a*(z)^(2)]*Erfc[Sqrt[a]*z]</code> || Successful || Failure || - || <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[z, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[-1, Power[Power[a, -1], Rational[1, 2]], Power[E, Times[a, Power[z, 2]]], Power[Pi, Rational[1, 2]], Erfc[Times[Power[a, Rational[1, 2]], z]]], Times[Power[a, Rational[-1, 2]], Power[E, Times[a, Power[z, 2]]], Power[Pi, Rational[1, 2]], Power[z, -1], Power[Power[z, 2], Rational[1, 2]], Plus[-1, Times[Power[Power[z, -2], Rational[1, 2]], z], Erfc[Times[Power[a, Rational[1, 2]], z]]]]], And[Greater[Re[a], 0], Greater[Re[Power[z, 2]], 0]]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[a, Rational[1, 2]], Rule[z, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[-1, Power[Power[a, -1], Rational[1, 2]], Power[E, Times[a, Power[z, 2]]], Power[Pi, Rational[1, 2]], Erfc[Times[Power[a, Rational[1, 2]], z]]], Times[Power[a, Rational[-1, 2]], Power[E, Times[a, Power[z, 2]]], Power[Pi, Rational[1, 2]], Power[z, -1], Power[Power[z, 2], Rational[1, 2]], Plus[-1, Times[Power[Power[z, -2], Rational[1, 2]], z], Erfc[Times[Power[a, Rational[1, 2]], z]]]]], And[Greater[Re[a], 0], Greater[Re[Power[z, 2]], 0]]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[a, Rational[1, 2]], Rule[z, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[-1, Power[Power[a, -1], Rational[1, 2]], Power[E, Times[a, Power[z, 2]]], Power[Pi, Rational[1, 2]], Erfc[Times[Power[a, Rational[1, 2]], z]]], Times[Power[a, Rational[-1, 2]], Power[E, Times[a, Power[z, 2]]], Power[Pi, Rational[1, 2]], Power[z, -1], Power[Power[z, 2], Rational[1, 2]], Plus[-1, Times[Power[Power[z, -2], Rational[1, 2]], z], Erfc[Times[Power[a, Rational[1, 2]], z]]]]], And[Greater[Re[a], 0], Greater[Re[Power[z, 2]], 0]]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[a, Rational[1, 2]], Rule[z, Rational[1, 2]], Rule[ConditionalExpression[Plus[Times[-1, Power[Power[a, -1], Rational[1, 2]], Power[E, Times[a, Power[z, 2]]], Power[Pi, Rational[1, 2]], Erfc[Times[Power[a, Rational[1, 2]], z]]], Times[Power[a, Rational[-1, 2]], Power[E, Times[a, Power[z, 2]]], Power[Pi, Rational[1, 2]], Power[z, -1], Power[Power[z, 2], Rational[1, 2]], Plus[-1, Times[Power[Power[z, -2], Rational[1, 2]], z], Erfc[Times[Power[a, Rational[1, 2]], z]]]]], And[Greater[Re[a], 0], Greater[Re[Power[z, 2]], 0]]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
+
| [https://dlmf.nist.gov/7.7.E4 7.7.E4] || [[Item:Q2374|<math>\int_{0}^{\infty}\frac{e^{-at}}{\sqrt{t+z^{2}}}\diff{t} = \sqrt{\frac{\pi}{a}}e^{az^{2}}\erfc@{\sqrt{a}z}</math>]] || <code>int((exp(- a*t))/(sqrt(t + (z)^(2))), t = 0..infinity)=sqrt((Pi)/(a))*exp(a*(z)^(2))*erfc(sqrt(a)*z)</code> || <code>Integrate[Divide[Exp[- a*t],Sqrt[t + (z)^(2)]], {t, 0, Infinity}]=Sqrt[Divide[Pi,a]]*Exp[a*(z)^(2)]*Erfc[Sqrt[a]*z]</code> || Successful || Failure || - || Successful
 
|-
 
|-
| [https://dlmf.nist.gov/7.7.E6 7.7.E6] || [[Item:Q2376|<math>\int_{x}^{\infty}e^{-(at^{2}+2bt+c)}\diff{t} = \frac{1}{2}\sqrt{\frac{\pi}{a}}e^{(b^{2}-ac)/a}\erfc@{\sqrt{a}x+\frac{b}{\sqrt{a}}}</math>]] || <code>int(exp(-(a*(t)^(2)+ 2*b*t + c)), t = x..infinity)=(1)/(2)*sqrt((Pi)/(a))*exp(((b)^(2)- a*c)/ a)*erfc(sqrt(a)*x +(b)/(sqrt(a)))</code> || <code>Integrate[Exp[-(a*(t)^(2)+ 2*b*t + c)], {t, x, Infinity}]=Divide[1,2]*Sqrt[Divide[Pi,a]]*Exp[((b)^(2)- a*c)/ a]*Erfc[Sqrt[a]*x +Divide[b,Sqrt[a]]]</code> || Failure || Failure || Skip || Error
+
| [https://dlmf.nist.gov/7.7.E6 7.7.E6] || [[Item:Q2376|<math>\int_{x}^{\infty}e^{-(at^{2}+2bt+c)}\diff{t} = \frac{1}{2}\sqrt{\frac{\pi}{a}}e^{(b^{2}-ac)/a}\erfc@{\sqrt{a}x+\frac{b}{\sqrt{a}}}</math>]] || <code>int(exp(-(a*(t)^(2)+ 2*b*t + c)), t = x..infinity)=(1)/(2)*sqrt((Pi)/(a))*exp(((b)^(2)- a*c)/ a)*erfc(sqrt(a)*x +(b)/(sqrt(a)))</code> || <code>Integrate[Exp[-(a*(t)^(2)+ 2*b*t + c)], {t, x, Infinity}]=Divide[1,2]*Sqrt[Divide[Pi,a]]*Exp[((b)^(2)- a*c)/ a]*Erfc[Sqrt[a]*x +Divide[b,Sqrt[a]]]</code> || Failure || Failure || Skip || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/7.7.E7 7.7.E7] || [[Item:Q2377|<math>\int_{x}^{\infty}e^{-a^{2}t^{2}-(b^{2}/t^{2})}\diff{t} = \frac{\sqrt{\pi}}{4a}\left(e^{2ab}\erfc@{ax+(b/x)}+e^{-2ab}\erfc@{ax-(b/x)}\right)</math>]] || <code>int(exp(- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))), t = x..infinity)=(sqrt(Pi))/(4*a)*(exp(2*a*b)*erfc(a*x +(b/ x))+ exp(- 2*a*b)*erfc(a*x -(b/ x)))</code> || <code>Integrate[Exp[- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))], {t, x, Infinity}]=Divide[Sqrt[Pi],4*a]*(Exp[2*a*b]*Erfc[a*x +(b/ x)]+ Exp[- 2*a*b]*Erfc[a*x -(b/ x)])</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/7.7.E7 7.7.E7] || [[Item:Q2377|<math>\int_{x}^{\infty}e^{-a^{2}t^{2}-(b^{2}/t^{2})}\diff{t} = \frac{\sqrt{\pi}}{4a}\left(e^{2ab}\erfc@{ax+(b/x)}+e^{-2ab}\erfc@{ax-(b/x)}\right)</math>]] || <code>int(exp(- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))), t = x..infinity)=(sqrt(Pi))/(4*a)*(exp(2*a*b)*erfc(a*x +(b/ x))+ exp(- 2*a*b)*erfc(a*x -(b/ x)))</code> || <code>Integrate[Exp[- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))], {t, x, Infinity}]=Divide[Sqrt[Pi],4*a]*(Exp[2*a*b]*Erfc[a*x +(b/ x)]+ Exp[- 2*a*b]*Erfc[a*x -(b/ x)])</code> || Failure || Failure || Skip || Error  
 
|-
 
|-
| [https://dlmf.nist.gov/7.7.E8 7.7.E8] || [[Item:Q2378|<math>\int_{0}^{\infty}e^{-a^{2}t^{2}-(b^{2}/t^{2})}\diff{t} = \frac{\sqrt{\pi}}{2a}e^{-2ab}</math>]] || <code>int(exp(- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))), t = 0..infinity)=(sqrt(Pi))/(2*a)*exp(- 2*a*b)</code> || <code>Integrate[Exp[- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))], {t, 0, Infinity}]=Divide[Sqrt[Pi],2*a]*Exp[- 2*a*b]</code> || Successful || Failure || - || Error
+
| [https://dlmf.nist.gov/7.7.E8 7.7.E8] || [[Item:Q2378|<math>\int_{0}^{\infty}e^{-a^{2}t^{2}-(b^{2}/t^{2})}\diff{t} = \frac{\sqrt{\pi}}{2a}e^{-2ab}</math>]] || <code>int(exp(- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))), t = 0..infinity)=(sqrt(Pi))/(2*a)*exp(- 2*a*b)</code> || <code>Integrate[Exp[- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))], {t, 0, Infinity}]=Divide[Sqrt[Pi],2*a]*Exp[- 2*a*b]</code> || Successful || Failure || - || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/7.7.E9 7.7.E9] || [[Item:Q2379|<math>\int_{0}^{x}\erf@@{t}\diff{t} = x\erf@@{x}+\frac{1}{\sqrt{\pi}}\left(e^{-x^{2}}-1\right)</math>]] || <code>int(erf(t), t = 0..x)= x*erf(x)+(1)/(sqrt(Pi))*(exp(- (x)^(2))- 1)</code> || <code>Integrate[Erf[t], {t, 0, x}]= x*Erf[x]+Divide[1,Sqrt[Pi]]*(Exp[- (x)^(2)]- 1)</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/7.7.E9 7.7.E9] || [[Item:Q2379|<math>\int_{0}^{x}\erf@@{t}\diff{t} = x\erf@@{x}+\frac{1}{\sqrt{\pi}}\left(e^{-x^{2}}-1\right)</math>]] || <code>int(erf(t), t = 0..x)= x*erf(x)+(1)/(sqrt(Pi))*(exp(- (x)^(2))- 1)</code> || <code>Integrate[Erf[t], {t, 0, x}]= x*Erf[x]+Divide[1,Sqrt[Pi]]*(Exp[- (x)^(2)]- 1)</code> || Successful || Successful || - || -  
Line 101: Line 101:
 
| [https://dlmf.nist.gov/7.7.E11 7.7.E11] || [[Item:Q2381|<math>\auxFresnelg@{z} = \frac{1}{\pi\sqrt{2}}\int_{0}^{\infty}\frac{\sqrt{t}e^{-\pi z^{2}t/2}}{t^{2}+1}\diff{t}</math>]] || <code>Fresnelg(z)=(1)/(Pi*sqrt(2))*int((sqrt(t)*exp(- Pi*(z)^(2)* t/ 2))/((t)^(2)+ 1), t = 0..infinity)</code> || <code>FresnelG[z]=Divide[1,Pi*Sqrt[2]]*Integrate[Divide[Sqrt[t]*Exp[- Pi*(z)^(2)* t/ 2],(t)^(2)+ 1], {t, 0, Infinity}]</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/7.7.E11 7.7.E11] || [[Item:Q2381|<math>\auxFresnelg@{z} = \frac{1}{\pi\sqrt{2}}\int_{0}^{\infty}\frac{\sqrt{t}e^{-\pi z^{2}t/2}}{t^{2}+1}\diff{t}</math>]] || <code>Fresnelg(z)=(1)/(Pi*sqrt(2))*int((sqrt(t)*exp(- Pi*(z)^(2)* t/ 2))/((t)^(2)+ 1), t = 0..infinity)</code> || <code>FresnelG[z]=Divide[1,Pi*Sqrt[2]]*Integrate[Divide[Sqrt[t]*Exp[- Pi*(z)^(2)* t/ 2],(t)^(2)+ 1], {t, 0, Infinity}]</code> || Failure || Failure || Skip || Error  
 
|-
 
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| [https://dlmf.nist.gov/7.7.E12 7.7.E12] || [[Item:Q2382|<math>\auxFresnelg@{z}+i\auxFresnelf@{z} = e^{-\pi iz^{2}/2}\int_{z}^{\infty}e^{\pi it^{2}/2}\diff{t}</math>]] || <code>Fresnelg(z)+ I*Fresnelf(z)= exp(- Pi*I*(z)^(2)/ 2)*int(exp(Pi*I*(t)^(2)/ 2), t = z..infinity)</code> || <code>FresnelG[z]+ I*FresnelF[z]= Exp[- Pi*I*(z)^(2)/ 2]*Integrate[Exp[Pi*I*(t)^(2)/ 2], {t, z, Infinity}]</code> || Failure || Failure || Skip || Skip
+
| [https://dlmf.nist.gov/7.7.E12 7.7.E12] || [[Item:Q2382|<math>\auxFresnelg@{z}+i\auxFresnelf@{z} = e^{-\pi iz^{2}/2}\int_{z}^{\infty}e^{\pi it^{2}/2}\diff{t}</math>]] || <code>Fresnelg(z)+ I*Fresnelf(z)= exp(- Pi*I*(z)^(2)/ 2)*int(exp(Pi*I*(t)^(2)/ 2), t = z..infinity)</code> || <code>FresnelG[z]+ I*FresnelF[z]= Exp[- Pi*I*(z)^(2)/ 2]*Integrate[Exp[Pi*I*(t)^(2)/ 2], {t, z, Infinity}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.12449815517713354, 0.12449815517716199] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.12449815517710515, -0.12449815517713354] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
 
|-
 
|-
 
| [https://dlmf.nist.gov/7.7.E13 7.7.E13] || [[Item:Q2383|<math>\auxFresnelf@{z} = \frac{(2\pi)^{-3/2}}{2\pi i}\int_{c-i\infty}^{c+i\infty}\zeta^{-s}\EulerGamma@{s}\EulerGamma@{s+\tfrac{1}{2}}\*\EulerGamma@{s+\tfrac{3}{4}}\EulerGamma@{\tfrac{1}{4}-s}\diff{s}</math>]] || <code>Fresnelf(z)=((2*Pi)^(- 3/ 2))/(2*Pi*I)*int((zeta)^(- s)* GAMMA(s)*GAMMA(s +(1)/(2))* GAMMA(s +(3)/(4))*GAMMA((1)/(4)- s), s = c - I*infinity..c + I*infinity)</code> || <code>FresnelF[z]=Divide[(2*Pi)^(- 3/ 2),2*Pi*I]*Integrate[(\[zeta])^(- s)* Gamma[s]*Gamma[s +Divide[1,2]]* Gamma[s +Divide[3,4]]*Gamma[Divide[1,4]- s], {s, c - I*Infinity, c + I*Infinity}]</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/7.7.E13 7.7.E13] || [[Item:Q2383|<math>\auxFresnelf@{z} = \frac{(2\pi)^{-3/2}}{2\pi i}\int_{c-i\infty}^{c+i\infty}\zeta^{-s}\EulerGamma@{s}\EulerGamma@{s+\tfrac{1}{2}}\*\EulerGamma@{s+\tfrac{3}{4}}\EulerGamma@{\tfrac{1}{4}-s}\diff{s}</math>]] || <code>Fresnelf(z)=((2*Pi)^(- 3/ 2))/(2*Pi*I)*int((zeta)^(- s)* GAMMA(s)*GAMMA(s +(1)/(2))* GAMMA(s +(3)/(4))*GAMMA((1)/(4)- s), s = c - I*infinity..c + I*infinity)</code> || <code>FresnelF[z]=Divide[(2*Pi)^(- 3/ 2),2*Pi*I]*Integrate[(\[zeta])^(- s)* Gamma[s]*Gamma[s +Divide[1,2]]* Gamma[s +Divide[3,4]]*Gamma[Divide[1,4]- s], {s, c - I*Infinity, c + I*Infinity}]</code> || Failure || Failure || Skip || Error  
Line 115: Line 115:
 
| [https://dlmf.nist.gov/7.8.E5 7.8.E5] || [[Item:Q2391|<math>\frac{x^{2}}{2x^{2}+1} <= \frac{x^{2}(2x^{2}+5)}{4x^{4}+12x^{2}+3}</math>]] || <code>((x)^(2))/(2*(x)^(2)+ 1)< =((x)^(2)*(2*(x)^(2)+ 5))/(4*(x)^(4)+ 12*(x)^(2)+ 3)</code> || <code>Divide[(x)^(2),2*(x)^(2)+ 1]< =Divide[(x)^(2)*(2*(x)^(2)+ 5),4*(x)^(4)+ 12*(x)^(2)+ 3]</code> || Failure || Failure || Successful || Successful  
 
| [https://dlmf.nist.gov/7.8.E5 7.8.E5] || [[Item:Q2391|<math>\frac{x^{2}}{2x^{2}+1} <= \frac{x^{2}(2x^{2}+5)}{4x^{4}+12x^{2}+3}</math>]] || <code>((x)^(2))/(2*(x)^(2)+ 1)< =((x)^(2)*(2*(x)^(2)+ 5))/(4*(x)^(4)+ 12*(x)^(2)+ 3)</code> || <code>Divide[(x)^(2),2*(x)^(2)+ 1]< =Divide[(x)^(2)*(2*(x)^(2)+ 5),4*(x)^(4)+ 12*(x)^(2)+ 3]</code> || Failure || Failure || Successful || Successful  
 
|-
 
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| [https://dlmf.nist.gov/7.8.E5 7.8.E5] || [[Item:Q2391|<math>\frac{2x^{4}+9x^{2}+4}{4x^{4}+20x^{2}+15} < \frac{x^{2}+1}{2x^{2}+3}</math>]] || <code>(2*(x)^(4)+ 9*(x)^(2)+ 4)/(4*(x)^(4)+ 20*(x)^(2)+ 15)<((x)^(2)+ 1)/(2*(x)^(2)+ 3)</code> || <code>Divide[2*(x)^(4)+ 9*(x)^(2)+ 4,4*(x)^(4)+ 20*(x)^(2)+ 15]<Divide[(x)^(2)+ 1,2*(x)^(2)+ 3]</code> || Failure || Failure || Skip || Skip
+
| [https://dlmf.nist.gov/7.8.E5 7.8.E5] || [[Item:Q2391|<math>\frac{2x^{4}+9x^{2}+4}{4x^{4}+20x^{2}+15} < \frac{x^{2}+1}{2x^{2}+3}</math>]] || <code>(2*(x)^(4)+ 9*(x)^(2)+ 4)/(4*(x)^(4)+ 20*(x)^(2)+ 15)<((x)^(2)+ 1)/(2*(x)^(2)+ 3)</code> || <code>Divide[2*(x)^(4)+ 9*(x)^(2)+ 4,4*(x)^(4)+ 20*(x)^(2)+ 15]<Divide[(x)^(2)+ 1,2*(x)^(2)+ 3]</code> || Failure || Failure || Skip || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/7.8.E6 7.8.E6] || [[Item:Q2392|<math>\int_{0}^{x}e^{at^{2}}\diff{t} < \frac{1}{3ax}\left(2e^{ax^{2}}+ax^{2}-2\right)</math>]] || <code>int(exp(a*(t)^(2)), t = 0..x)<(1)/(3*a*x)*(2*exp(a*(x)^(2))+ a*(x)^(2)- 2)</code> || <code>Integrate[Exp[a*(t)^(2)], {t, 0, x}]<Divide[1,3*a*x]*(2*Exp[a*(x)^(2)]+ a*(x)^(2)- 2)</code> || Error || Failure || - || Successful  
 
| [https://dlmf.nist.gov/7.8.E6 7.8.E6] || [[Item:Q2392|<math>\int_{0}^{x}e^{at^{2}}\diff{t} < \frac{1}{3ax}\left(2e^{ax^{2}}+ax^{2}-2\right)</math>]] || <code>int(exp(a*(t)^(2)), t = 0..x)<(1)/(3*a*x)*(2*exp(a*(x)^(2))+ a*(x)^(2)- 2)</code> || <code>Integrate[Exp[a*(t)^(2)], {t, 0, x}]<Divide[1,3*a*x]*(2*Exp[a*(x)^(2)]+ a*(x)^(2)- 2)</code> || Error || Failure || - || Successful  
Line 151: Line 151:
 
| [https://dlmf.nist.gov/7.11.E8 7.11.E8] || [[Item:Q2410|<math>\Fresnelsinint@{z} = \tfrac{1}{6}\pi z^{3}\genhyperF{1}{2}@{\tfrac{3}{4}}{\tfrac{7}{4},\tfrac{3}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}</math>]] || <code>FresnelS(z)=(1)/(6)*Pi*(z)^(3)* hypergeom([(3)/(4)], [(7)/(4),(3)/(2)], -(1)/(16)*(Pi)^(2)* (z)^(4))</code> || <code>FresnelS[z]=Divide[1,6]*Pi*(z)^(3)* HypergeometricPFQ[{Divide[3,4]}, {Divide[7,4],Divide[3,2]}, -Divide[1,16]*(Pi)^(2)* (z)^(4)]</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/7.11.E8 7.11.E8] || [[Item:Q2410|<math>\Fresnelsinint@{z} = \tfrac{1}{6}\pi z^{3}\genhyperF{1}{2}@{\tfrac{3}{4}}{\tfrac{7}{4},\tfrac{3}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}</math>]] || <code>FresnelS(z)=(1)/(6)*Pi*(z)^(3)* hypergeom([(3)/(4)], [(7)/(4),(3)/(2)], -(1)/(16)*(Pi)^(2)* (z)^(4))</code> || <code>FresnelS[z]=Divide[1,6]*Pi*(z)^(3)* HypergeometricPFQ[{Divide[3,4]}, {Divide[7,4],Divide[3,2]}, -Divide[1,16]*(Pi)^(2)* (z)^(4)]</code> || Successful || Successful || - || -  
 
|-
 
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| [https://dlmf.nist.gov/7.13#Ex4 7.13#Ex4] || [[Item:Q2422|<math>\mu = \ln@{\lambda\sqrt{2\pi}}</math>]] || <code>mu = ln(lambda*sqrt(2*Pi))</code> || <code>\[Mu]= Log[\[Lambda]*Sqrt[2*Pi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.197872151+.6288153986*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2)}</code><br><code>-.197872151-2.199611725*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.026299275-2.199611725*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.026299275+.6288153986*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = -2^(1/2)+I*2^(1/2)}</code><br><code>-.197872151+2.199611725*I <- {lambda = 2^(1/2)-I*2^(1/2), mu = 2^(1/2)+I*2^(1/2)}</code><br><code>-.197872151-.6288153986*I <- {lambda = 2^(1/2)-I*2^(1/2), mu = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.026299275-.6288153986*I <- {lambda = 2^(1/2)-I*2^(1/2), mu = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.026299275+2.199611725*I <- {lambda = 2^(1/2)-I*2^(1/2), mu = -2^(1/2)+I*2^(1/2)}</code><br><code>-.197872151+3.770408052*I <- {lambda = -2^(1/2)-I*2^(1/2), mu = 2^(1/2)+I*2^(1/2)}</code><br><code>-.197872151+.941980928*I <- {lambda = -2^(1/2)-I*2^(1/2), mu = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.026299275+.941980928*I <- {lambda = -2^(1/2)-I*2^(1/2), mu = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.026299275+3.770408052*I <- {lambda = -2^(1/2)-I*2^(1/2), mu = -2^(1/2)+I*2^(1/2)}</code><br><code>-.197872151-.941980928*I <- {lambda = -2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2)}</code><br><code>-.197872151-3.770408052*I <- {lambda = -2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.026299275-3.770408052*I <- {lambda = -2^(1/2)+I*2^(1/2), mu = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.026299275-.941980928*I <- {lambda = -2^(1/2)+I*2^(1/2), mu = -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[-0.1978721513915227, 0.6288153989756469] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.1978721513915227, -2.199611725770543] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.026299276137713, -2.199611725770543] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.026299276137713, 0.6288153989756469] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.1978721513915227, 2.199611725770543] <- {Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.1978721513915227, -0.6288153989756469] <- {Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.026299276137713, -0.6288153989756469] <- {Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.026299276137713, 2.199611725770543] <- {Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.1978721513915227, 3.7704080525654398] <- {Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.1978721513915227, 0.9419809278192497] <- {Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.026299276137713, 0.9419809278192497] <- {Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.026299276137713, 3.7704080525654398] <- {Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.1978721513915227, -0.9419809278192497] <- {Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.1978721513915227, -3.7704080525654398] <- {Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.026299276137713, -3.7704080525654398] <- {Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.026299276137713, -0.9419809278192497] <- {Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/7.13#Ex4 7.13#Ex4] || [[Item:Q2422|<math>\mu = \ln@{\lambda\sqrt{2\pi}}</math>]] || <code>mu = ln(lambda*sqrt(2*Pi))</code> || <code>\[Mu]= Log[\[Lambda]*Sqrt[2*Pi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.197872151+.6288153986*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2)}</code><br><code>-.197872151-2.199611725*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.026299275-2.199611725*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.026299275+.6288153986*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = -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[-0.1978721513915227, 0.6288153989756469] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.1978721513915227, -2.199611725770543] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.026299276137713, -2.199611725770543] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.026299276137713, 0.6288153989756469] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
| [https://dlmf.nist.gov/7.13#Ex8 7.13#Ex8] || [[Item:Q2426|<math>\mu = \ln@{2\lambda\sqrt{2\pi}}</math>]] || <code>mu = ln(2*lambda*sqrt(2*Pi))</code> || <code>\[Mu]= Log[2*\[Lambda]*Sqrt[2*Pi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.891019332+.6288153986*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2)}</code><br><code>-.891019332-2.199611725*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.719446456-2.199611725*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.719446456+.6288153986*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = -2^(1/2)+I*2^(1/2)}</code><br><code>-.891019332+2.199611725*I <- {lambda = 2^(1/2)-I*2^(1/2), mu = 2^(1/2)+I*2^(1/2)}</code><br><code>-.891019332-.6288153986*I <- {lambda = 2^(1/2)-I*2^(1/2), mu = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.719446456-.6288153986*I <- {lambda = 2^(1/2)-I*2^(1/2), mu = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.719446456+2.199611725*I <- {lambda = 2^(1/2)-I*2^(1/2), mu = -2^(1/2)+I*2^(1/2)}</code><br><code>-.891019332+3.770408052*I <- {lambda = -2^(1/2)-I*2^(1/2), mu = 2^(1/2)+I*2^(1/2)}</code><br><code>-.891019332+.941980928*I <- {lambda = -2^(1/2)-I*2^(1/2), mu = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.719446456+.941980928*I <- {lambda = -2^(1/2)-I*2^(1/2), mu = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.719446456+3.770408052*I <- {lambda = -2^(1/2)-I*2^(1/2), mu = -2^(1/2)+I*2^(1/2)}</code><br><code>-.891019332-.941980928*I <- {lambda = -2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2)}</code><br><code>-.891019332-3.770408052*I <- {lambda = -2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.719446456-3.770408052*I <- {lambda = -2^(1/2)+I*2^(1/2), mu = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.719446456-.941980928*I <- {lambda = -2^(1/2)+I*2^(1/2), mu = -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[-0.8910193319514683, 0.6288153989756469] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8910193319514683, -2.199611725770543] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.719446456697659, -2.199611725770543] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.719446456697659, 0.6288153989756469] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8910193319514683, 2.199611725770543] <- {Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8910193319514683, -0.6288153989756469] <- {Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.719446456697659, -0.6288153989756469] <- {Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.719446456697659, 2.199611725770543] <- {Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8910193319514683, 3.7704080525654398] <- {Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8910193319514683, 0.9419809278192497] <- {Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.719446456697659, 0.9419809278192497] <- {Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.719446456697659, 3.7704080525654398] <- {Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8910193319514683, -0.9419809278192497] <- {Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8910193319514683, -3.7704080525654398] <- {Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.719446456697659, -3.7704080525654398] <- {Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.719446456697659, -0.9419809278192497] <- {Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/7.13#Ex8 7.13#Ex8] || [[Item:Q2426|<math>\mu = \ln@{2\lambda\sqrt{2\pi}}</math>]] || <code>mu = ln(2*lambda*sqrt(2*Pi))</code> || <code>\[Mu]= Log[2*\[Lambda]*Sqrt[2*Pi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-.891019332+.6288153986*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2)}</code><br><code>-.891019332-2.199611725*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.719446456-2.199611725*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.719446456+.6288153986*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = -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[-0.8910193319514683, 0.6288153989756469] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8910193319514683, -2.199611725770543] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.719446456697659, -2.199611725770543] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.719446456697659, 0.6288153989756469] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
| [https://dlmf.nist.gov/7.13#Ex12 7.13#Ex12] || [[Item:Q2430|<math>\alpha = (2/\pi)\ln@{\pi\lambda}</math>]] || <code>alpha =(2/ Pi)* ln(Pi*lambda)</code> || <code>\[Alpha]=(2/ Pi)* Log[Pi*\[Lambda]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.244184683+.9142135621*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2)}</code><br><code>.244184683+1.914213562*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)-I*2^(1/2)}</code><br><code>.244184683+2.914213561*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = -2^(1/2)-I*2^(1/2)}</code><br><code>.244184683-.85786437e-1*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = -2^(1/2)+I*2^(1/2)}</code><br><code>.244184683-1.914213562*I <- {alpha = 2^(1/2)-I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2)}</code><br><code>.244184683-.9142135621*I <- {alpha = 2^(1/2)-I*2^(1/2), lambda = 2^(1/2)-I*2^(1/2)}</code><br><code>.244184683+.85786437e-1*I <- {alpha = 2^(1/2)-I*2^(1/2), lambda = -2^(1/2)-I*2^(1/2)}</code><br><code>.244184683-2.914213561*I <- {alpha = 2^(1/2)-I*2^(1/2), lambda = -2^(1/2)+I*2^(1/2)}</code><br><code>-2.584242441-1.914213562*I <- {alpha = -2^(1/2)-I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2)}</code><br><code>-2.584242441-.9142135621*I <- {alpha = -2^(1/2)-I*2^(1/2), lambda = 2^(1/2)-I*2^(1/2)}</code><br><code>-2.584242441+.85786437e-1*I <- {alpha = -2^(1/2)-I*2^(1/2), lambda = -2^(1/2)-I*2^(1/2)}</code><br><code>-2.584242441-2.914213561*I <- {alpha = -2^(1/2)-I*2^(1/2), lambda = -2^(1/2)+I*2^(1/2)}</code><br><code>-2.584242441+.9142135621*I <- {alpha = -2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2)}</code><br><code>-2.584242441+1.914213562*I <- {alpha = -2^(1/2)+I*2^(1/2), lambda = 2^(1/2)-I*2^(1/2)}</code><br><code>-2.584242441+2.914213561*I <- {alpha = -2^(1/2)+I*2^(1/2), lambda = -2^(1/2)-I*2^(1/2)}</code><br><code>-2.584242441-.85786437e-1*I <- {alpha = -2^(1/2)+I*2^(1/2), lambda = -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[0.24418468271597948, 0.9142135623730951] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, 1.9142135623730951] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, 2.914213562373095] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, -0.08578643762690485] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, -1.9142135623730951] <- {Rule[α, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, -0.9142135623730951] <- {Rule[α, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, 0.08578643762690485] <- {Rule[α, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, -2.914213562373095] <- {Rule[α, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, -1.9142135623730951] <- {Rule[α, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, -0.9142135623730951] <- {Rule[α, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, 0.08578643762690485] <- {Rule[α, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, -2.914213562373095] <- {Rule[α, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, 0.9142135623730951] <- {Rule[α, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, 1.9142135623730951] <- {Rule[α, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, 2.914213562373095] <- {Rule[α, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, -0.08578643762690485] <- {Rule[α, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/7.13#Ex12 7.13#Ex12] || [[Item:Q2430|<math>\alpha = (2/\pi)\ln@{\pi\lambda}</math>]] || <code>alpha =(2/ Pi)* ln(Pi*lambda)</code> || <code>\[Alpha]=(2/ Pi)* Log[Pi*\[Lambda]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.244184683+.9142135621*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2)}</code><br><code>.244184683+1.914213562*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)-I*2^(1/2)}</code><br><code>.244184683+2.914213561*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = -2^(1/2)-I*2^(1/2)}</code><br><code>.244184683-.85786437e-1*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = -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[0.24418468271597948, 0.9142135623730951] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, 1.9142135623730951] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, 2.914213562373095] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, -0.08578643762690485] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
| [https://dlmf.nist.gov/7.13#Ex14 7.13#Ex14] || [[Item:Q2432|<math>\alpha = (2/\pi)\ln@{\pi\lambda}</math>]] || <code>alpha =(2/ Pi)* ln(Pi*lambda)</code> || <code>\[Alpha]=(2/ Pi)* Log[Pi*\[Lambda]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.244184683+.9142135621*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2)}</code><br><code>.244184683+1.914213562*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)-I*2^(1/2)}</code><br><code>.244184683+2.914213561*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = -2^(1/2)-I*2^(1/2)}</code><br><code>.244184683-.85786437e-1*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = -2^(1/2)+I*2^(1/2)}</code><br><code>.244184683-1.914213562*I <- {alpha = 2^(1/2)-I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2)}</code><br><code>.244184683-.9142135621*I <- {alpha = 2^(1/2)-I*2^(1/2), lambda = 2^(1/2)-I*2^(1/2)}</code><br><code>.244184683+.85786437e-1*I <- {alpha = 2^(1/2)-I*2^(1/2), lambda = -2^(1/2)-I*2^(1/2)}</code><br><code>.244184683-2.914213561*I <- {alpha = 2^(1/2)-I*2^(1/2), lambda = -2^(1/2)+I*2^(1/2)}</code><br><code>-2.584242441-1.914213562*I <- {alpha = -2^(1/2)-I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2)}</code><br><code>-2.584242441-.9142135621*I <- {alpha = -2^(1/2)-I*2^(1/2), lambda = 2^(1/2)-I*2^(1/2)}</code><br><code>-2.584242441+.85786437e-1*I <- {alpha = -2^(1/2)-I*2^(1/2), lambda = -2^(1/2)-I*2^(1/2)}</code><br><code>-2.584242441-2.914213561*I <- {alpha = -2^(1/2)-I*2^(1/2), lambda = -2^(1/2)+I*2^(1/2)}</code><br><code>-2.584242441+.9142135621*I <- {alpha = -2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2)}</code><br><code>-2.584242441+1.914213562*I <- {alpha = -2^(1/2)+I*2^(1/2), lambda = 2^(1/2)-I*2^(1/2)}</code><br><code>-2.584242441+2.914213561*I <- {alpha = -2^(1/2)+I*2^(1/2), lambda = -2^(1/2)-I*2^(1/2)}</code><br><code>-2.584242441-.85786437e-1*I <- {alpha = -2^(1/2)+I*2^(1/2), lambda = -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[0.24418468271597948, 0.9142135623730951] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, 1.9142135623730951] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, 2.914213562373095] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, -0.08578643762690485] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, -1.9142135623730951] <- {Rule[α, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, -0.9142135623730951] <- {Rule[α, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, 0.08578643762690485] <- {Rule[α, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, -2.914213562373095] <- {Rule[α, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, -1.9142135623730951] <- {Rule[α, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, -0.9142135623730951] <- {Rule[α, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, 0.08578643762690485] <- {Rule[α, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, -2.914213562373095] <- {Rule[α, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, 0.9142135623730951] <- {Rule[α, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, 1.9142135623730951] <- {Rule[α, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, 2.914213562373095] <- {Rule[α, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.584242442030211, -0.08578643762690485] <- {Rule[α, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/7.13#Ex14 7.13#Ex14] || [[Item:Q2432|<math>\alpha = (2/\pi)\ln@{\pi\lambda}</math>]] || <code>alpha =(2/ Pi)* ln(Pi*lambda)</code> || <code>\[Alpha]=(2/ Pi)* Log[Pi*\[Lambda]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.244184683+.9142135621*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2)}</code><br><code>.244184683+1.914213562*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)-I*2^(1/2)}</code><br><code>.244184683+2.914213561*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = -2^(1/2)-I*2^(1/2)}</code><br><code>.244184683-.85786437e-1*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = -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[0.24418468271597948, 0.9142135623730951] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, 1.9142135623730951] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, 2.914213562373095] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24418468271597948, -0.08578643762690485] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
 
| [https://dlmf.nist.gov/7.14.E1 7.14.E1] || [[Item:Q2433|<math>\int_{0}^{\infty}e^{2iat}\erfc@{bt}\diff{t} = {\frac{1}{a\sqrt{\pi}}\DawsonsintF@{\frac{a}{b}}+\frac{i}{2a}\left(1-e^{-(a/b)^{2}}\right)}</math>]] || <code>int(exp(2*I*a*t)*erfc(b*t), t = 0..infinity)=(1)/(a*sqrt(Pi))*dawson((a)/(b))+(I)/(2*a)*(1 - exp(-(a/ b)^(2)))</code> || <code>Integrate[Exp[2*I*a*t]*Erfc[b*t], {t, 0, Infinity}]=Divide[1,a*Sqrt[Pi]]*DawsonF[Divide[a,b]]+Divide[I,2*a]*(1 - Exp[-(a/ b)^(2)])</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/7.14.E1 7.14.E1] || [[Item:Q2433|<math>\int_{0}^{\infty}e^{2iat}\erfc@{bt}\diff{t} = {\frac{1}{a\sqrt{\pi}}\DawsonsintF@{\frac{a}{b}}+\frac{i}{2a}\left(1-e^{-(a/b)^{2}}\right)}</math>]] || <code>int(exp(2*I*a*t)*erfc(b*t), t = 0..infinity)=(1)/(a*sqrt(Pi))*dawson((a)/(b))+(I)/(2*a)*(1 - exp(-(a/ b)^(2)))</code> || <code>Integrate[Exp[2*I*a*t]*Erfc[b*t], {t, 0, Infinity}]=Divide[1,a*Sqrt[Pi]]*DawsonF[Divide[a,b]]+Divide[I,2*a]*(1 - Exp[-(a/ b)^(2)])</code> || Failure || Failure || Skip || Error  
Line 165: Line 165:
 
| [https://dlmf.nist.gov/7.14.E4 7.14.E4] || [[Item:Q2436|<math>\int_{0}^{\infty}e^{(a-b)t}\erfc@{\sqrt{at}+\sqrt{\frac{c}{t}}}\diff{t} = \frac{e^{-2(\sqrt{ac}+\sqrt{bc})}}{\sqrt{b}(\sqrt{a}+\sqrt{b})}</math>]] || <code>int(exp((a - b)* t)*erfc(sqrt(a*t)+sqrt((c)/(t))), t = 0..infinity)=(exp(- 2*(sqrt(a*c)+sqrt(b*c))))/(sqrt(b)*(sqrt(a)+sqrt(b)))</code> || <code>Integrate[Exp[(a - b)* t]*Erfc[Sqrt[a*t]+Sqrt[Divide[c,t]]], {t, 0, Infinity}]=Divide[Exp[- 2*(Sqrt[a*c]+Sqrt[b*c])],Sqrt[b]*(Sqrt[a]+Sqrt[b])]</code> || Failure || Failure || Skip || Error  
 
| [https://dlmf.nist.gov/7.14.E4 7.14.E4] || [[Item:Q2436|<math>\int_{0}^{\infty}e^{(a-b)t}\erfc@{\sqrt{at}+\sqrt{\frac{c}{t}}}\diff{t} = \frac{e^{-2(\sqrt{ac}+\sqrt{bc})}}{\sqrt{b}(\sqrt{a}+\sqrt{b})}</math>]] || <code>int(exp((a - b)* t)*erfc(sqrt(a*t)+sqrt((c)/(t))), t = 0..infinity)=(exp(- 2*(sqrt(a*c)+sqrt(b*c))))/(sqrt(b)*(sqrt(a)+sqrt(b)))</code> || <code>Integrate[Exp[(a - b)* t]*Erfc[Sqrt[a*t]+Sqrt[Divide[c,t]]], {t, 0, Infinity}]=Divide[Exp[- 2*(Sqrt[a*c]+Sqrt[b*c])],Sqrt[b]*(Sqrt[a]+Sqrt[b])]</code> || Failure || Failure || Skip || Error  
 
|-
 
|-
| [https://dlmf.nist.gov/7.14.E5 7.14.E5] || [[Item:Q2437|<math>\int_{0}^{\infty}e^{-at}\Fresnelcosint@{t}\diff{t} = \frac{1}{a}\auxFresnelf@{\frac{a}{\pi}}</math>]] || <code>int(exp(- a*t)*FresnelC(t), t = 0..infinity)=(1)/(a)*Fresnelf((a)/(Pi))</code> || <code>Integrate[Exp[- a*t]*FresnelC[t], {t, 0, Infinity}]=Divide[1,a]*FresnelF[Divide[a,Pi]]</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, Power[a, -1], FresnelF[Times[a, Power[Pi, -1]]]], Times[Rational[1, 2], Power[a, -1], Plus[Times[Cos[Times[Rational[1, 2], Power[a, 2], Power[Pi, -1]]], Plus[1, Times[-2, FresnelS[Times[a, Power[Pi, -1]]]]]], Times[Plus[-1, Times[2, FresnelC[Times[a, Power[Pi, -1]]]]], Sin[Times[Rational[1, 2], Power[a, 2], Power[Pi, -1]]]]]]], 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, Power[a, -1], FresnelF[Times[a, Power[Pi, -1]]]], Times[Rational[1, 2], Power[a, -1], Plus[Times[Cos[Times[Rational[1, 2], Power[a, 2], Power[Pi, -1]]], Plus[1, Times[-2, FresnelS[Times[a, Power[Pi, -1]]]]]], Times[Plus[-1, Times[2, FresnelC[Times[a, Power[Pi, -1]]]]], Sin[Times[Rational[1, 2], Power[a, 2], Power[Pi, -1]]]]]]], 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, Power[a, -1], FresnelF[Times[a, Power[Pi, -1]]]], Times[Rational[1, 2], Power[a, -1], Plus[Times[Cos[Times[Rational[1, 2], Power[a, 2], Power[Pi, -1]]], Plus[1, Times[-2, FresnelS[Times[a, Power[Pi, -1]]]]]], Times[Plus[-1, Times[2, FresnelC[Times[a, Power[Pi, -1]]]]], Sin[Times[Rational[1, 2], Power[a, 2], Power[Pi, -1]]]]]]], 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, Power[a, -1], FresnelF[Times[a, Power[Pi, -1]]]], Times[Rational[1, 2], Power[a, -1], Plus[Times[Cos[Times[Rational[1, 2], Power[a, 2], Power[Pi, -1]]], Plus[1, Times[-2, FresnelS[Times[a, Power[Pi, -1]]]]]], Times[Plus[-1, Times[2, FresnelC[Times[a, Power[Pi, -1]]]]], Sin[Times[Rational[1, 2], Power[a, 2], Power[Pi, -1]]]]]]], Greater[Re[a], 0]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>
+
| [https://dlmf.nist.gov/7.14.E5 7.14.E5] || [[Item:Q2437|<math>\int_{0}^{\infty}e^{-at}\Fresnelcosint@{t}\diff{t} = \frac{1}{a}\auxFresnelf@{\frac{a}{\pi}}</math>]] || <code>int(exp(- a*t)*FresnelC(t), t = 0..infinity)=(1)/(a)*Fresnelf((a)/(Pi))</code> || <code>Integrate[Exp[- a*t]*FresnelC[t], {t, 0, Infinity}]=Divide[1,a]*FresnelF[Divide[a,Pi]]</code> || Failure || Failure || Skip || Successful
 
|-
 
|-
| [https://dlmf.nist.gov/7.14.E6 7.14.E6] || [[Item:Q2438|<math>\int_{0}^{\infty}e^{-at}\Fresnelsinint@{t}\diff{t} = \frac{1}{a}\auxFresnelg@{\frac{a}{\pi}}</math>]] || <code>int(exp(- a*t)*FresnelS(t), t = 0..infinity)=(1)/(a)*Fresnelg((a)/(Pi))</code> || <code>Integrate[Exp[- a*t]*FresnelS[t], {t, 0, Infinity}]=Divide[1,a]*FresnelG[Divide[a,Pi]]</code> || Failure || Failure || Skip || Skip
+
| [https://dlmf.nist.gov/7.14.E6 7.14.E6] || [[Item:Q2438|<math>\int_{0}^{\infty}e^{-at}\Fresnelsinint@{t}\diff{t} = \frac{1}{a}\auxFresnelg@{\frac{a}{\pi}}</math>]] || <code>int(exp(- a*t)*FresnelS(t), t = 0..infinity)=(1)/(a)*Fresnelg((a)/(Pi))</code> || <code>Integrate[Exp[- a*t]*FresnelS[t], {t, 0, Infinity}]=Divide[1,a]*FresnelG[Divide[a,Pi]]</code> || Failure || Failure || Skip || Successful
 
|-
 
|-
 
| [https://dlmf.nist.gov/7.17#Ex1 7.17#Ex1] || [[Item:Q2441|<math>y = \inverf@@{x}</math>]] || <code>Error</code> || <code>y = InverseErf[x]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>DirectedInfinity[-1] <- {Rule[x, 1], Rule[y, 1]}</code><br><code>DirectedInfinity[-1] <- {Rule[x, 1], Rule[y, 2]}</code><br><code>DirectedInfinity[-1] <- {Rule[x, 1], Rule[y, 3]}</code><br></div></div>  
 
| [https://dlmf.nist.gov/7.17#Ex1 7.17#Ex1] || [[Item:Q2441|<math>y = \inverf@@{x}</math>]] || <code>Error</code> || <code>y = InverseErf[x]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>DirectedInfinity[-1] <- {Rule[x, 1], Rule[y, 1]}</code><br><code>DirectedInfinity[-1] <- {Rule[x, 1], Rule[y, 2]}</code><br><code>DirectedInfinity[-1] <- {Rule[x, 1], Rule[y, 3]}</code><br></div></div>  
 
|-
 
|-
| [https://dlmf.nist.gov/7.17#Ex2 7.17#Ex2] || [[Item:Q2442|<math>y = \inverfc@@{x}</math>]] || <code>Error</code> || <code>y = InverseErfc[x]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.0 <- {Rule[x, 1], Rule[y, 1]}</code><br><code>2.0 <- {Rule[x, 1], Rule[y, 2]}</code><br><code>3.0 <- {Rule[x, 1], Rule[y, 3]}</code><br><code>DirectedInfinity[1] <- {Rule[x, 2], Rule[y, 1]}</code><br><code>DirectedInfinity[1] <- {Rule[x, 2], Rule[y, 2]}</code><br><code>DirectedInfinity[1] <- {Rule[x, 2], Rule[y, 3]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/7.17#Ex2 7.17#Ex2] || [[Item:Q2442|<math>y = \inverfc@@{x}</math>]] || <code>Error</code> || <code>y = InverseErfc[x]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.0 <- {Rule[x, 1], Rule[y, 1]}</code><br><code>2.0 <- {Rule[x, 1], Rule[y, 2]}</code><br><code>3.0 <- {Rule[x, 1], Rule[y, 3]}</code><br><code>DirectedInfinity[1] <- {Rule[x, 2], Rule[y, 1]}</code><br>... skip entries to safe data<br></div></div>  
 
|-
 
|-
 
| [https://dlmf.nist.gov/7.18#Ex1 7.18#Ex1] || [[Item:Q2450|<math>\repinterfc{-1}@{z} = \frac{2}{\sqrt{\pi}}e^{-z^{2}}</math>]] || <code>erfc(- 1, z)=(2)/(sqrt(Pi))*exp(- (z)^(2))</code> || <code>I^(- 1)*Erfc[z]=Divide[2,Sqrt[Pi]]*Exp[- (z)^(2)]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.011483603950918, -0.8436484572858769] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.46363208502383696, 0.8642718813368542] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.46363208502383696, -2.864271881336854] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.011483603950918, -1.1563515427141229] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
 
| [https://dlmf.nist.gov/7.18#Ex1 7.18#Ex1] || [[Item:Q2450|<math>\repinterfc{-1}@{z} = \frac{2}{\sqrt{\pi}}e^{-z^{2}}</math>]] || <code>erfc(- 1, z)=(2)/(sqrt(Pi))*exp(- (z)^(2))</code> || <code>I^(- 1)*Erfc[z]=Divide[2,Sqrt[Pi]]*Exp[- (z)^(2)]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.011483603950918, -0.8436484572858769] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.46363208502383696, 0.8642718813368542] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.46363208502383696, -2.864271881336854] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.011483603950918, -1.1563515427141229] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
Line 177: Line 177:
 
| [https://dlmf.nist.gov/7.18#Ex2 7.18#Ex2] || [[Item:Q2451|<math>\repinterfc{0}@{z} = \erfc@@{z}</math>]] || <code>erfc(0, z)= erfc(z)</code> || <code>I^(0)*Erfc[z]= Erfc[z]</code> || Successful || Successful || - || -  
 
| [https://dlmf.nist.gov/7.18#Ex2 7.18#Ex2] || [[Item:Q2451|<math>\repinterfc{0}@{z} = \erfc@@{z}</math>]] || <code>erfc(0, z)= erfc(z)</code> || <code>I^(0)*Erfc[z]= Erfc[z]</code> || Successful || Successful || - || -  
 
|-
 
|-
| [https://dlmf.nist.gov/7.18.E2 7.18.E2] || [[Item:Q2452|<math>\repinterfc{n}@{z} = \int_{z}^{\infty}\repinterfc{n-1}@{t}\diff{t}</math>]] || <code>erfc(n, z)= int(erfc(n - 1, t), t = z..infinity)</code> || <code>I^(n)*Erfc[z]= Integrate[I^(n - 1)*Erfc[t], {t, z, Infinity}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.30711932433427286, -0.06448523556221403] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.06448523556221401, -0.30711932433427286] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.30711932433427286, 0.06448523556221403] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.2407321945928082, 0.04386181151123664] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.04386181151123665, 0.2407321945928082] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.2407321945928082, -0.04386181151123664] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.587694930153382, -0.8722889362574269] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8722889362574269, -2.587694930153382] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.587694930153382, 0.8722889362574269] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.135546449080463, 4.892912360308404] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.892912360308404, -3.135546449080463] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.135546449080463, -4.892912360308404] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/7.18.E2 7.18.E2] || [[Item:Q2452|<math>\repinterfc{n}@{z} = \int_{z}^{\infty}\repinterfc{n-1}@{t}\diff{t}</math>]] || <code>erfc(n, z)= int(erfc(n - 1, t), t = z..infinity)</code> || <code>I^(n)*Erfc[z]= Integrate[I^(n - 1)*Erfc[t], {t, z, Infinity}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.30711932433427286, -0.06448523556221403] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.06448523556221401, -0.30711932433427286] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.30711932433427286, 0.06448523556221403] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.2407321945928082, 0.04386181151123664] <- {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/7.18.E2 7.18.E2] || [[Item:Q2452|<math>\int_{z}^{\infty}\repinterfc{n-1}@{t}\diff{t} = \frac{2}{\sqrt{\pi}}\int_{z}^{\infty}\frac{(t-z)^{n}}{n!}e^{-t^{2}}\diff{t}</math>]] || <code>int(erfc(n - 1, t), t = z..infinity)=(2)/(sqrt(Pi))*int(((t - z)^(n))/(factorial(n))*exp(- (t)^(2)), t = z..infinity)</code> || <code>Integrate[I^(n - 1)*Erfc[t], {t, z, Infinity}]=Divide[2,Sqrt[Pi]]*Integrate[Divide[(t - z)^(n),(n)!]*Exp[- (t)^(2)], {t, z, Infinity}]</code> || Failure || Failure || Skip || Skip
+
| [https://dlmf.nist.gov/7.18.E2 7.18.E2] || [[Item:Q2452|<math>\int_{z}^{\infty}\repinterfc{n-1}@{t}\diff{t} = \frac{2}{\sqrt{\pi}}\int_{z}^{\infty}\frac{(t-z)^{n}}{n!}e^{-t^{2}}\diff{t}</math>]] || <code>int(erfc(n - 1, t), t = z..infinity)=(2)/(sqrt(Pi))*int(((t - z)^(n))/(factorial(n))*exp(- (t)^(2)), t = z..infinity)</code> || <code>Integrate[I^(n - 1)*Erfc[t], {t, z, Infinity}]=Divide[2,Sqrt[Pi]]*Integrate[Divide[(t - z)^(n),(n)!]*Exp[- (t)^(2)], {t, z, Infinity}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.06643066657209085, 0.02648998567028575] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.036107850584238765, -0.054264273946754926] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.04191638050136022, 0.039897144071178225] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.03610785058423853, 0.054264273946755606] <- {Rule[n, 3], 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/7.18.E3 7.18.E3] || [[Item:Q2453|<math>\deriv{}{z}\repinterfc{n}@{z} = -\repinterfc{n-1}@{z}</math>]] || <code>diff(erfc(n, z), z)= - erfc(n - 1, z)</code> || <code>D[I^(n)*Erfc[z], z]= - I^(n - 1)*Erfc[z]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.8436484572858769, -1.011483603950918] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8642718813368542, -0.46363208502383696] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.864271881336854, -0.46363208502383696] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1563515427141229, -1.011483603950918] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
 
| [https://dlmf.nist.gov/7.18.E3 7.18.E3] || [[Item:Q2453|<math>\deriv{}{z}\repinterfc{n}@{z} = -\repinterfc{n-1}@{z}</math>]] || <code>diff(erfc(n, z), z)= - erfc(n - 1, z)</code> || <code>D[I^(n)*Erfc[z], z]= - I^(n - 1)*Erfc[z]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.8436484572858769, -1.011483603950918] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8642718813368542, -0.46363208502383696] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.864271881336854, -0.46363208502383696] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1563515427141229, -1.011483603950918] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
Line 187: Line 187:
 
| [https://dlmf.nist.gov/7.18.E5 7.18.E5] || [[Item:Q2455|<math>\deriv[2]{W}{z}+2z\deriv{W}{z}-2nW = 0</math>]] || <code>diff(W, [z$(2)])+ 2*z*diff(W, z)- 2*n*W = 0</code> || <code>D[W, {z, 2}]+ 2*z*D[W, z]- 2*n*W = 0</code> || Failure || Failure || Skip || Successful  
 
| [https://dlmf.nist.gov/7.18.E5 7.18.E5] || [[Item:Q2455|<math>\deriv[2]{W}{z}+2z\deriv{W}{z}-2nW = 0</math>]] || <code>diff(W, [z$(2)])+ 2*z*diff(W, z)- 2*n*W = 0</code> || <code>D[W, {z, 2}]+ 2*z*D[W, z]- 2*n*W = 0</code> || Failure || Failure || Skip || Successful  
 
|-
 
|-
| [https://dlmf.nist.gov/7.18.E6 7.18.E6] || [[Item:Q2456|<math>\repinterfc{n}@{z} = \sum_{k=0}^{\infty}\frac{(-1)^{k}z^{k}}{2^{n-k}k!\EulerGamma@{1+\frac{1}{2}(n-k)}}</math>]] || <code>erfc(n, z)= sum(((- 1)^(k)* (z)^(k))/((2)^(n - k)* factorial(k)*GAMMA(1 +(1)/(2)*(n - k))), k = 0..infinity)</code> || <code>I^(n)*Erfc[z]= Sum[Divide[(- 1)^(k)* (z)^(k),(2)^(n - k)* (k)!*Gamma[1 +Divide[1,2]*(n - k)]], {k, 0, Infinity}]</code> || Failure || Failure || Skip || Error
+
| [https://dlmf.nist.gov/7.18.E6 7.18.E6] || [[Item:Q2456|<math>\repinterfc{n}@{z} = \sum_{k=0}^{\infty}\frac{(-1)^{k}z^{k}}{2^{n-k}k!\EulerGamma@{1+\frac{1}{2}(n-k)}}</math>]] || <code>erfc(n, z)= sum(((- 1)^(k)* (z)^(k))/((2)^(n - k)* factorial(k)*GAMMA(1 +(1)/(2)*(n - k))), k = 0..infinity)</code> || <code>I^(n)*Erfc[z]= Sum[Divide[(- 1)^(k)* (z)^(k),(2)^(n - k)* (k)!*Gamma[1 +Divide[1,2]*(n - k)]], {k, 0, Infinity}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.3071193243342728, -0.06448523556221496] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.0019454310098768, -0.280629338663987] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.2710114737500341, 0.01022096161545949] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24073219459280773, 0.043861811511237594] <- {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/7.18.E7 7.18.E7] || [[Item:Q2457|<math>\repinterfc{n}@{z} = -\frac{z}{n}\repinterfc{n-1}@{z}+\frac{1}{2n}\repinterfc{n-2}@{z}</math>]] || <code>erfc(n, z)= -(z)/(n)*erfc(n - 1, z)+(1)/(2*n)*erfc(n - 2, z)</code> || <code>I^(n)*Erfc[z]= -Divide[z,n]*I^(n - 1)*Erfc[z]+Divide[1,2*n]*I^(n - 2)*Erfc[z]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.45357088174560434, -0.11223852300991567] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.18558922366932362, 0.1362991844027226] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7572198179127398, -1.5268234761539925] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3963799233276677, -3.163903851905481] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
 
| [https://dlmf.nist.gov/7.18.E7 7.18.E7] || [[Item:Q2457|<math>\repinterfc{n}@{z} = -\frac{z}{n}\repinterfc{n-1}@{z}+\frac{1}{2n}\repinterfc{n-2}@{z}</math>]] || <code>erfc(n, z)= -(z)/(n)*erfc(n - 1, z)+(1)/(2*n)*erfc(n - 2, z)</code> || <code>I^(n)*Erfc[z]= -Divide[z,n]*I^(n - 1)*Erfc[z]+Divide[1,2*n]*I^(n - 2)*Erfc[z]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.45357088174560434, -0.11223852300991567] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.18558922366932362, 0.1362991844027226] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7572198179127398, -1.5268234761539925] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3963799233276677, -3.163903851905481] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
 
|-
 
|-
| [https://dlmf.nist.gov/7.18.E8 7.18.E8] || [[Item:Q2458|<math>(-1)^{n}\repinterfc{n}@{z}+\repinterfc{n}@{-z} = \frac{i^{-n}}{2^{n-1}n!}\HermitepolyH{n}@{iz}</math>]] || <code>(- 1)^(n)* erfc(n, z)+ erfc(n, - z)=((I)^(- n))/((2)^(n - 1)* factorial(n))*HermiteH(n, I*z)</code> || <code>(- 1)^(n)* I^(n)*Erfc[z]+ I^(n)*Erfc[- z]=Divide[(I)^(- n),(2)^(n - 1)* (n)!]*HermiteH[n, I*z]</code> || Failure || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-2.280575605819109, -0.8078037006952131] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5, -4.0] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6306597830504983, -4.613348288401651] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.3762786436732717, 4.849050548797168] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5, 4.0] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.7263628209046602, 0.5721014402996966] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.280575605819109, 0.8078037006952131] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5, -4.0] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6306597830504983, 4.613348288401651] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.3762786436732717, -4.849050548797168] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5, 4.0] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.7263628209046602, -0.5721014402996966] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/7.18.E8 7.18.E8] || [[Item:Q2458|<math>(-1)^{n}\repinterfc{n}@{z}+\repinterfc{n}@{-z} = \frac{i^{-n}}{2^{n-1}n!}\HermitepolyH{n}@{iz}</math>]] || <code>(- 1)^(n)* erfc(n, z)+ erfc(n, - z)=((I)^(- n))/((2)^(n - 1)* factorial(n))*HermiteH(n, I*z)</code> || <code>(- 1)^(n)* I^(n)*Erfc[z]+ I^(n)*Erfc[- z]=Divide[(I)^(- n),(2)^(n - 1)* (n)!]*HermiteH[n, I*z]</code> || Failure || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-2.280575605819109, -0.8078037006952131] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5, -4.0] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6306597830504983, -4.613348288401651] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.3762786436732717, 4.849050548797168] <- {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/7.18.E9 7.18.E9] || [[Item:Q2459|<math>\repinterfc{n}@{z} = e^{-z^{2}}\left(\frac{1}{2^{n}\EulerGamma@{\tfrac{1}{2}n+1}}\KummerconfhyperM@{\tfrac{1}{2}n+\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}}-\frac{z}{2^{n-1}\EulerGamma@{\tfrac{1}{2}n+\tfrac{1}{2}}}\KummerconfhyperM@{\tfrac{1}{2}n+1}{\tfrac{3}{2}}{z^{2}}\right)</math>]] || <code>erfc(n, z)= exp(- (z)^(2))*((1)/((2)^(n)* GAMMA((1)/(2)*n + 1))*KummerM((1)/(2)*n +(1)/(2), (1)/(2), (z)^(2))-(z)/((2)^(n - 1)* GAMMA((1)/(2)*n +(1)/(2)))*KummerM((1)/(2)*n + 1, (3)/(2), (z)^(2)))</code> || <code>I^(n)*Erfc[z]= Exp[- (z)^(2)]*(Divide[1,(2)^(n)* Gamma[Divide[1,2]*n + 1]]*Hypergeometric1F1[Divide[1,2]*n +Divide[1,2], Divide[1,2], (z)^(2)]-Divide[z,(2)^(n - 1)* Gamma[Divide[1,2]*n +Divide[1,2]]]*Hypergeometric1F1[Divide[1,2]*n + 1, Divide[3,2], (z)^(2)])</code> || Failure || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.3071193243342726, -0.06448523556221446] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.0019454310098766699, -0.28062933866398737] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.27101147375003376, 0.010220961615459446] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.2407321945928081, 0.04386181151123732] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.0019454310098763125, 0.28062933866398676] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.2768400451770471, 0.010402462435518562] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.587694930153382, -0.8722889362574278] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.498054568990123, -3.7193706613360122] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.9016712568005321, -4.603127326786192] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.135546449080463, 4.892912360308404] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.4980545689901237, 3.7193706613360127] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4495227757276135, 0.5825039027352155] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/7.18.E9 7.18.E9] || [[Item:Q2459|<math>\repinterfc{n}@{z} = e^{-z^{2}}\left(\frac{1}{2^{n}\EulerGamma@{\tfrac{1}{2}n+1}}\KummerconfhyperM@{\tfrac{1}{2}n+\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}}-\frac{z}{2^{n-1}\EulerGamma@{\tfrac{1}{2}n+\tfrac{1}{2}}}\KummerconfhyperM@{\tfrac{1}{2}n+1}{\tfrac{3}{2}}{z^{2}}\right)</math>]] || <code>erfc(n, z)= exp(- (z)^(2))*((1)/((2)^(n)* GAMMA((1)/(2)*n + 1))*KummerM((1)/(2)*n +(1)/(2), (1)/(2), (z)^(2))-(z)/((2)^(n - 1)* GAMMA((1)/(2)*n +(1)/(2)))*KummerM((1)/(2)*n + 1, (3)/(2), (z)^(2)))</code> || <code>I^(n)*Erfc[z]= Exp[- (z)^(2)]*(Divide[1,(2)^(n)* Gamma[Divide[1,2]*n + 1]]*Hypergeometric1F1[Divide[1,2]*n +Divide[1,2], Divide[1,2], (z)^(2)]-Divide[z,(2)^(n - 1)* Gamma[Divide[1,2]*n +Divide[1,2]]]*Hypergeometric1F1[Divide[1,2]*n + 1, Divide[3,2], (z)^(2)])</code> || Failure || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.3071193243342726, -0.06448523556221446] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.0019454310098766699, -0.28062933866398737] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.27101147375003376, 0.010220961615459446] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.2407321945928081, 0.04386181151123732] <- {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/7.18.E10 7.18.E10] || [[Item:Q2460|<math>\repinterfc{n}@{z} = \frac{e^{-z^{2}}}{2^{n}\sqrt{\pi}}\KummerconfhyperU@{\tfrac{1}{2}n+\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}}</math>]] || <code>erfc(n, z)=(exp(- (z)^(2)))/((2)^(n)*sqrt(Pi))*KummerU((1)/(2)*n +(1)/(2), (1)/(2), (z)^(2))</code> || <code>I^(n)*Erfc[z]=Divide[Exp[- (z)^(2)],(2)^(n)*Sqrt[Pi]]*HypergeometricU[Divide[1,2]*n +Divide[1,2], Divide[1,2], (z)^(2)]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>2.828427124+2.828427124*I <- {z = -2^(1/2)-I*2^(1/2), n = 1}</code><br><code>.4754857140+3.986592840*I <- {z = -2^(1/2)-I*2^(1/2), n = 2}</code><br><code>-1.178511301+2.592724863*I <- {z = -2^(1/2)-I*2^(1/2), n = 3}</code><br><code>2.828427124-2.828427124*I <- {z = -2^(1/2)+I*2^(1/2), n = 1}</code><br><code>.4754857140-3.986592840*I <- {z = -2^(1/2)+I*2^(1/2), n = 2}</code><br><code>-1.178511301-2.592724863*I <- {z = -2^(1/2)+I*2^(1/2), n = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.30711932433427297, -0.06448523556221639] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.0019454310098774158, -0.28062933866398587] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.2710114737500343, 0.010220961615459385] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24073219459280773, 0.04386181151123868] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.0019454310098774158, 0.28062933866398587] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.27684004517704724, 0.010402462435518383] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.2407321945928081, 1.9561381884887608] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.0225688550608547, 0.2672221802630952] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.27684004517704675, -2.010402462435518] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3071193243342733, 2.064485235562216] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.0225688550608547, -0.2672221802630952] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.2710114737500338, -2.0102209616154587] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/7.18.E10 7.18.E10] || [[Item:Q2460|<math>\repinterfc{n}@{z} = \frac{e^{-z^{2}}}{2^{n}\sqrt{\pi}}\KummerconfhyperU@{\tfrac{1}{2}n+\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}}</math>]] || <code>erfc(n, z)=(exp(- (z)^(2)))/((2)^(n)*sqrt(Pi))*KummerU((1)/(2)*n +(1)/(2), (1)/(2), (z)^(2))</code> || <code>I^(n)*Erfc[z]=Divide[Exp[- (z)^(2)],(2)^(n)*Sqrt[Pi]]*HypergeometricU[Divide[1,2]*n +Divide[1,2], Divide[1,2], (z)^(2)]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>2.828427124+2.828427124*I <- {z = -2^(1/2)-I*2^(1/2), n = 1}</code><br><code>.4754857140+3.986592840*I <- {z = -2^(1/2)-I*2^(1/2), n = 2}</code><br><code>-1.178511301+2.592724863*I <- {z = -2^(1/2)-I*2^(1/2), n = 3}</code><br><code>2.828427124-2.828427124*I <- {z = -2^(1/2)+I*2^(1/2), n = 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[-0.30711932433427297, -0.06448523556221639] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.0019454310098774158, -0.28062933866398587] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.2710114737500343, 0.010220961615459385] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24073219459280773, 0.04386181151123868] <- {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/7.18.E11 7.18.E11] || [[Item:Q2461|<math>\repinterfc{n}@{z} = \frac{e^{-z^{2}/2}}{\sqrt{2^{n-1}\pi}}\paraU@{n+\tfrac{1}{2}}{z\sqrt{2}}</math>]] || <code>erfc(n, z)=(exp(- (z)^(2)/ 2))/(sqrt((2)^(n - 1)* Pi))*CylinderU(n +(1)/(2), z*sqrt(2))</code> || <code>I^(n)*Erfc[z]=Divide[Exp[- (z)^(2)/ 2],Sqrt[(2)^(n - 1)* Pi]]*ParabolicCylinderD[-n +Divide[1,2] - 1/2, z*Sqrt[2]]</code> || Failure || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.26663427796467404, -0.20400647408383285] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.013159682786361896, -0.3122322253171296] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.2652586505052597, 0.005571565714632675] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.281217240962407, 0.18338305003285552] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.013159682786361896, 0.3122322253171296] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.28259286842182135, 0.015051858336344684] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1475792844084207, 2.2040064740838328] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.03378310683734, -1.7643807063900485] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6188120410985343, -4.833998690460822] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6954308033355017, 1.816616949967144] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.03378310683734, 1.7643807063900485] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.07096052217145316, 0.8133752664098455] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/7.18.E11 7.18.E11] || [[Item:Q2461|<math>\repinterfc{n}@{z} = \frac{e^{-z^{2}/2}}{\sqrt{2^{n-1}\pi}}\paraU@{n+\tfrac{1}{2}}{z\sqrt{2}}</math>]] || <code>erfc(n, z)=(exp(- (z)^(2)/ 2))/(sqrt((2)^(n - 1)* Pi))*CylinderU(n +(1)/(2), z*sqrt(2))</code> || <code>I^(n)*Erfc[z]=Divide[Exp[- (z)^(2)/ 2],Sqrt[(2)^(n - 1)* Pi]]*ParabolicCylinderD[-n +Divide[1,2] - 1/2, z*Sqrt[2]]</code> || Failure || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-0.26663427796467404, -0.20400647408383285] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.013159682786361896, -0.3122322253171296] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.2652586505052597, 0.005571565714632675] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.281217240962407, 0.18338305003285552] <- {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/7.20.E1 7.20.E1] || [[Item:Q2479|<math>\frac{1}{\sigma\sqrt{2\pi}}\int_{-\infty}^{x}e^{-(t-m)^{2}/(2\sigma^{2})}\diff{t} = \frac{1}{2}\erfc@{\frac{m-x}{\sigma\sqrt{2}}}</math>]] || <code>(1)/(sigma*sqrt(2*Pi))*int(exp(-(t - m)^(2)/(2*(sigma)^(2))), t = - infinity..x)=(1)/(2)*erfc((m - x)/(sigma*sqrt(2)))</code> || <code>Divide[1,\[Sigma]*Sqrt[2*Pi]]*Integrate[Exp[-(t - m)^(2)/(2*(\[Sigma])^(2))], {t, - Infinity, x}]=Divide[1,2]*Erfc[Divide[m - x,\[Sigma]*Sqrt[2]]]</code> || Failure || Failure || Skip || Error
+
| [https://dlmf.nist.gov/7.20.E1 7.20.E1] || [[Item:Q2479|<math>\frac{1}{\sigma\sqrt{2\pi}}\int_{-\infty}^{x}e^{-(t-m)^{2}/(2\sigma^{2})}\diff{t} = \frac{1}{2}\erfc@{\frac{m-x}{\sigma\sqrt{2}}}</math>]] || <code>(1)/(sigma*sqrt(2*Pi))*int(exp(-(t - m)^(2)/(2*(sigma)^(2))), t = - infinity..x)=(1)/(2)*erfc((m - x)/(sigma*sqrt(2)))</code> || <code>Divide[1,\[Sigma]*Sqrt[2*Pi]]*Integrate[Exp[-(t - m)^(2)/(2*(\[Sigma])^(2))], {t, - Infinity, x}]=Divide[1,2]*Erfc[Divide[m - x,\[Sigma]*Sqrt[2]]]</code> || Failure || Failure || Skip || Successful
 
|-
 
|-
| [https://dlmf.nist.gov/7.20.E1 7.20.E1] || [[Item:Q2479|<math>\frac{1}{2}\erfc@{\frac{m-x}{\sigma\sqrt{2}}} = Q\left(\frac{m-x}{\sigma}\right)</math>]] || <code>(1)/(2)*erfc((m - x)/(sigma*sqrt(2)))= Q*((m - x)/(sigma))</code> || <code>Divide[1,2]*Erfc[Divide[m - x,\[Sigma]*Sqrt[2]]]= Q*(Divide[m - x,\[Sigma]])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.5000000000 <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 1, x = 1}</code><br><code>1.646697588-.1349567498*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 1, x = 2}</code><br><code>2.821306458-.2289406972*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 1, x = 3}</code><br><code>-.6466975876+.1349567498*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 2, x = 2}</code><br><code>1.646697588-.1349567498*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 2, x = 3}</code><br><code>-1.821306457+.2289406972*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 3, x = 1}</code><br><code>-.6466975876+.1349567498*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 3, x = 3}</code><br><code>.5000000000 <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 1, x = 1}</code><br><code>.6466975875+1.134956750*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 1, x = 2}</code><br><code>.8213064575+2.228940697*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 1, x = 3}</code><br><code>.3533024124-1.134956750*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 2, x = 2}</code><br><code>.6466975875+1.134956750*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 2, x = 3}</code><br><code>.1786935426-2.228940697*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 3, x = 1}</code><br><code>.3533024124-1.134956750*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 3, x = 3}</code><br><code>.5000000000 <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 1, x = 1}</code><br><code>-.6466975876+.1349567498*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 1, x = 2}</code><br><code>-1.821306457+.2289406972*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 1, x = 3}</code><br><code>1.646697588-.1349567498*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 2, x = 2}</code><br><code>-.6466975876+.1349567498*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 2, x = 3}</code><br><code>2.821306458-.2289406972*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 3, x = 1}</code><br><code>1.646697588-.1349567498*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 3, x = 3}</code><br><code>.5000000000 <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 1, x = 1}</code><br><code>.3533024124-1.134956750*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 1, x = 2}</code><br><code>.1786935426-2.228940697*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 1, x = 3}</code><br><code>.6466975875+1.134956750*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 2, x = 2}</code><br><code>.3533024124-1.134956750*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 2, x = 3}</code><br><code>.8213064575+2.228940697*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 3, x = 1}</code><br><code>.6466975875+1.134956750*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 3, x = 3}</code><br><code>.5000000000 <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 1, x = 1}</code><br><code>.6466975875-1.134956750*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 1, x = 2}</code><br><code>.8213064575-2.228940697*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 1, x = 3}</code><br><code>.3533024124+1.134956750*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 2, x = 2}</code><br><code>.6466975875-1.134956750*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 2, x = 3}</code><br><code>.1786935426+2.228940697*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 3, x = 1}</code><br><code>.3533024124+1.134956750*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 3, x = 3}</code><br><code>.5000000000 <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 1, x = 1}</code><br><code>1.646697588+.1349567498*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 1, x = 2}</code><br><code>2.821306458+.2289406972*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 1, x = 3}</code><br><code>-.6466975876-.1349567498*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 2, x = 2}</code><br><code>1.646697588+.1349567498*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 2, x = 3}</code><br><code>-1.821306457-.2289406972*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 3, x = 1}</code><br><code>-.6466975876-.1349567498*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = 2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 3, x = 3}</code><br><code>.5000000000 <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 1, x = 1}</code><br><code>.3533024124+1.134956750*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 1, x = 2}</code><br><code>.1786935426+2.228940697*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 1, x = 3}</code><br><code>.6466975875-1.134956750*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 2, x = 2}</code><br><code>.3533024124+1.134956750*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 2, x = 3}</code><br><code>.8213064575-2.228940697*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 3, x = 1}</code><br><code>.6466975875-1.134956750*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 3, x = 3}</code><br><code>.5000000000 <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 1, x = 1}</code><br><code>-.6466975876-.1349567498*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 1, x = 2}</code><br><code>-1.821306457-.2289406972*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 1, x = 3}</code><br><code>1.646697588+.1349567498*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 2, x = 2}</code><br><code>-.6466975876-.1349567498*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 2, x = 3}</code><br><code>2.821306458+.2289406972*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 3, x = 1}</code><br><code>1.646697588+.1349567498*I <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = 2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 3, x = 3}</code><br><code>.5000000000 <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 1, x = 1}</code><br><code>-.3533024125-.1349567498*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 1, x = 2}</code><br><code>-1.178693542-.2289406972*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 1, x = 3}</code><br><code>1.353302412+.1349567498*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 2, x = 2}</code><br><code>-.3533024125-.1349567498*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 2, x = 3}</code><br><code>2.178693543+.2289406972*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 3, x = 1}</code><br><code>1.353302412+.1349567498*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 3, x = 3}</code><br><code>.5000000000 <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 1, x = 1}</code><br><code>.6466975875-.8650432502*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 1, x = 2}</code><br><code>.8213064575-1.771059303*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 1, x = 3}</code><br><code>.3533024124+.8650432502*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 2, x = 2}</code><br><code>.6466975875-.8650432502*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 2, x = 3}</code><br><code>.1786935426+1.771059303*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 3, x = 1}</code><br><code>.3533024124+.8650432502*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = -2^(1/2)-I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 3, x = 3}</code><br><code>.5000000000 <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 1, x = 1}</code><br><code>1.353302412+.1349567498*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 1, x = 2}</code><br><code>2.178693543+.2289406972*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 1, x = 3}</code><br><code>-.3533024125-.1349567498*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 2, x = 2}</code><br><code>1.353302412+.1349567498*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 2, x = 3}</code><br><code>-1.178693542-.2289406972*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 3, x = 1}</code><br><code>-.3533024125-.1349567498*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 3, x = 3}</code><br><code>.5000000000 <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 1, x = 1}</code><br><code>.3533024124+.8650432502*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 1, x = 2}</code><br><code>.1786935426+1.771059303*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 1, x = 3}</code><br><code>.6466975875-.8650432502*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 2, x = 2}</code><br><code>.3533024124+.8650432502*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 2, x = 3}</code><br><code>.8213064575-1.771059303*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 3, x = 1}</code><br><code>.6466975875-.8650432502*I <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = -2^(1/2)-I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 3, x = 3}</code><br><code>.5000000000 <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 1, x = 1}</code><br><code>.6466975875+.8650432502*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 1, x = 2}</code><br><code>.8213064575+1.771059303*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 1, x = 3}</code><br><code>.3533024124-.8650432502*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 2, x = 2}</code><br><code>.6466975875+.8650432502*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 2, x = 3}</code><br><code>.1786935426-1.771059303*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 3, x = 1}</code><br><code>.3533024124-.8650432502*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 3, x = 3}</code><br><code>.5000000000 <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 1, x = 1}</code><br><code>-.3533024125+.1349567498*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 1, x = 2}</code><br><code>-1.178693542+.2289406972*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 1, x = 3}</code><br><code>1.353302412-.1349567498*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 2, x = 2}</code><br><code>-.3533024125+.1349567498*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 2, x = 3}</code><br><code>2.178693543-.2289406972*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 3, x = 1}</code><br><code>1.353302412-.1349567498*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = -2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2), m = 3, x = 3}</code><br><code>.5000000000 <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 1, x = 1}</code><br><code>.3533024124-.8650432502*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 1, x = 2}</code><br><code>.1786935426-1.771059303*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 1, x = 3}</code><br><code>.6466975875+.8650432502*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 2, x = 2}</code><br><code>.3533024124-.8650432502*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 2, x = 3}</code><br><code>.8213064575+1.771059303*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 3, x = 1}</code><br><code>.6466975875+.8650432502*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2), m = 3, x = 3}</code><br><code>.5000000000 <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 1, x = 1}</code><br><code>1.353302412-.1349567498*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 1, x = 2}</code><br><code>2.178693543-.2289406972*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 1, x = 3}</code><br><code>-.3533024125+.1349567498*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 2, x = 1}</code><br><code>.5000000000 <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 2, x = 2}</code><br><code>1.353302412-.1349567498*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 2, x = 3}</code><br><code>-1.178693542+.2289406972*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 3, x = 1}</code><br><code>-.3533024125+.1349567498*I <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 3, x = 2}</code><br><code>.5000000000 <- {Q = -2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2), m = 3, x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6466975876615073, -0.13495674973157074] <- {Rule[m, 1], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.8213064574274105, -0.22894069721759613] <- {Rule[m, 1], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6466975876615073, 0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6466975876615073, -0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.8213064574274103, 0.22894069721759613] <- {Rule[m, 3], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6466975876615073, 0.13495674973157074] <- {Rule[m, 3], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, 1.1349567497315707] <- {Rule[m, 1], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8213064574274103, 2.2289406972175962] <- {Rule[m, 1], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, -1.1349567497315707] <- {Rule[m, 2], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, 1.1349567497315707] <- {Rule[m, 2], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.17869354257258974, -2.2289406972175962] <- {Rule[m, 3], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, -1.1349567497315707] <- {Rule[m, 3], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6466975876615073, 0.13495674973157074] <- {Rule[m, 1], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.8213064574274103, 0.22894069721759613] <- {Rule[m, 1], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6466975876615073, -0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6466975876615073, 0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.8213064574274105, -0.22894069721759613] <- {Rule[m, 3], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6466975876615073, -0.13495674973157074] <- {Rule[m, 3], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, -1.1349567497315707] <- {Rule[m, 1], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.17869354257258974, -2.2289406972175962] <- {Rule[m, 1], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, 1.1349567497315707] <- {Rule[m, 2], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, -1.1349567497315707] <- {Rule[m, 2], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8213064574274103, 2.2289406972175962] <- {Rule[m, 3], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, 1.1349567497315707] <- {Rule[m, 3], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, -1.1349567497315707] <- {Rule[m, 1], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8213064574274103, -2.2289406972175962] <- {Rule[m, 1], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, 1.1349567497315707] <- {Rule[m, 2], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, -1.1349567497315707] <- {Rule[m, 2], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.17869354257258974, 2.2289406972175962] <- {Rule[m, 3], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, 1.1349567497315707] <- {Rule[m, 3], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6466975876615073, 0.13495674973157074] <- {Rule[m, 1], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.8213064574274105, 0.22894069721759613] <- {Rule[m, 1], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6466975876615073, -0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6466975876615073, 0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.8213064574274103, -0.22894069721759613] <- {Rule[m, 3], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6466975876615073, -0.13495674973157074] <- {Rule[m, 3], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, 1.1349567497315707] <- {Rule[m, 1], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.17869354257258974, 2.2289406972175962] <- {Rule[m, 1], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, -1.1349567497315707] <- {Rule[m, 2], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, 1.1349567497315707] <- {Rule[m, 2], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8213064574274103, -2.2289406972175962] <- {Rule[m, 3], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, -1.1349567497315707] <- {Rule[m, 3], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6466975876615073, -0.13495674973157074] <- {Rule[m, 1], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.8213064574274103, -0.22894069721759613] <- {Rule[m, 1], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6466975876615073, 0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6466975876615073, -0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.8213064574274105, 0.22894069721759613] <- {Rule[m, 3], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6466975876615073, 0.13495674973157074] <- {Rule[m, 3], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3533024123384927, -0.13495674973157074] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1786935425725897, -0.22894069721759613] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3533024123384927, 0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3533024123384927, -0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.1786935425725895, 0.22894069721759613] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3533024123384927, 0.13495674973157074] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, -0.8650432502684293] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8213064574274103, -1.7710593027824038] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, 0.8650432502684293] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, -0.8650432502684293] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.17869354257258974, 1.7710593027824038] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, 0.8650432502684293] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3533024123384927, 0.13495674973157074] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.1786935425725895, 0.22894069721759613] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3533024123384927, -0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3533024123384927, 0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1786935425725897, -0.22894069721759613] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3533024123384927, -0.13495674973157074] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, 0.8650432502684293] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.17869354257258974, 1.7710593027824038] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, -0.8650432502684293] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, 0.8650432502684293] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8213064574274103, -1.7710593027824038] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, -0.8650432502684293] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, 0.8650432502684293] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8213064574274103, 1.7710593027824038] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, -0.8650432502684293] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, 0.8650432502684293] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.17869354257258974, -1.7710593027824038] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, -0.8650432502684293] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3533024123384927, 0.13495674973157074] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1786935425725897, 0.22894069721759613] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3533024123384927, -0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3533024123384927, 0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.1786935425725895, -0.22894069721759613] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3533024123384927, -0.13495674973157074] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, -0.8650432502684293] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.17869354257258974, -1.7710593027824038] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, 0.8650432502684293] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.3533024123384927, -0.8650432502684293] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8213064574274103, 1.7710593027824038] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.6466975876615073, 0.8650432502684293] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3533024123384927, -0.13495674973157074] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.1786935425725895, -0.22894069721759613] <- {Rule[m, 1], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3533024123384927, 0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 2], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.3533024123384927, -0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1786935425725897, 0.22894069721759613] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.3533024123384927, 0.13495674973157074] <- {Rule[m, 3], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.5 <- {Rule[m, 3], Rule[Q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div>  
+
| [https://dlmf.nist.gov/7.20.E1 7.20.E1] || [[Item:Q2479|<math>\frac{1}{2}\erfc@{\frac{m-x}{\sigma\sqrt{2}}} = Q\left(\frac{m-x}{\sigma}\right)</math>]] || <code>(1)/(2)*erfc((m - x)/(sigma*sqrt(2)))= Q*((m - x)/(sigma))</code> || <code>Divide[1,2]*Erfc[Divide[m - x,\[Sigma]*Sqrt[2]]]= Q*(Divide[m - x,\[Sigma]])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.5000000000 <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 1, x = 1}</code><br><code>1.646697588-.1349567498*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 1, x = 2}</code><br><code>2.821306458-.2289406972*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 1, x = 3}</code><br><code>-.6466975876+.1349567498*I <- {Q = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2), m = 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>0.5 <- {Rule[m, 1], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6466975876615073, -0.13495674973157074] <- {Rule[m, 1], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.8213064574274105, -0.22894069721759613] <- {Rule[m, 1], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6466975876615073, 0.13495674973157074] <- {Rule[m, 2], Rule[Q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[σ, 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/7.20.E1 7.20.E1] || [[Item:Q2479|<math>Q\left(\frac{m-x}{\sigma}\right) = P\left(\frac{x-m}{\sigma}\right)</math>]] || <code>Q*((m - x)/(sigma))= P*((x - m)/(sigma))</code> || <code>Q*(Divide[m - x,\[Sigma]])= P*(Divide[x - m,\[Sigma]])</code> || Failure || Failure || Skip || Skip  
 
| [https://dlmf.nist.gov/7.20.E1 7.20.E1] || [[Item:Q2479|<math>Q\left(\frac{m-x}{\sigma}\right) = P\left(\frac{x-m}{\sigma}\right)</math>]] || <code>Q*((m - x)/(sigma))= P*((x - m)/(sigma))</code> || <code>Q*(Divide[m - x,\[Sigma]])= P*(Divide[x - m,\[Sigma]])</code> || Failure || Failure || Skip || Skip  
 
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Latest revision as of 12:44, 19 January 2020

DLMF Formula Maple Mathematica Symbolic
Maple
Symbolic
Mathematica
Numeric
Maple
Numeric
Mathematica
7.2.E1 erf(z)=(2)/(sqrt(Pi))*int(exp(- (t)^(2)), t = 0..z) Erf[z]=Divide[2,Sqrt[Pi]]*Integrate[Exp[- (t)^(2)], {t, 0, z}] Successful Successful - -
7.2.E2 erfc(z)=(2)/(sqrt(Pi))*int(exp(- (t)^(2)), t = z..infinity) Erfc[z]=Divide[2,Sqrt[Pi]]*Integrate[Exp[- (t)^(2)], {t, z, Infinity}] Successful Successful - -
7.2.E2 (2)/(sqrt(Pi))*int(exp(- (t)^(2)), t = z..infinity)= 1 - erf(z) Divide[2,Sqrt[Pi]]*Integrate[Exp[- (t)^(2)], {t, z, Infinity}]= 1 - Erf[z] Successful Successful - -
7.2.E3 exp(- (z)^(2))*(1 +(2*I)/(sqrt(Pi))*int(exp((t)^(2)), t = 0..z))= exp(- (z)^(2))*erfc(- I*z) Exp[- (z)^(2)]*(1 +Divide[2*I,Sqrt[Pi]]*Integrate[Exp[(t)^(2)], {t, 0, z}])= Exp[- (z)^(2)]*Erfc[- I*z] Successful Successful - -
7.2#Ex1 limit(erf(z), z = infinity)= 1 Limit[Erf[z], z -> Infinity]= 1 Successful Successful - -
7.2#Ex2 limit(erfc(z), z = infinity)= 0 Limit[Erfc[z], z -> Infinity]= 0 Successful Successful - -
7.2.E5 dawson(z)= exp(- (z)^(2))*int(exp((t)^(2)), t = 0..z) DawsonF[z]= Exp[- (z)^(2)]*Integrate[Exp[(t)^(2)], {t, 0, z}] Successful Successful - -
7.2.E7 FresnelC(z)= int(cos((1)/(2)*Pi*(t)^(2)), t = 0..z) FresnelC[z]= Integrate[Cos[Divide[1,2]*Pi*(t)^(2)], {t, 0, z}] Successful Successful - -
7.2.E8 FresnelS(z)= int(sin((1)/(2)*Pi*(t)^(2)), t = 0..z) FresnelS[z]= Integrate[Sin[Divide[1,2]*Pi*(t)^(2)], {t, 0, z}] Successful Successful - -
7.2#Ex3 limit(FresnelC(x), x = infinity)=(1)/(2) Limit[FresnelC[x], x -> Infinity]=Divide[1,2] Successful Successful - -
7.2#Ex4 limit(FresnelS(x), x = infinity)=(1)/(2) Limit[FresnelS[x], x -> Infinity]=Divide[1,2] Successful Successful - -
7.2.E10 Fresnelf(z)=((1)/(2)- FresnelS(z))* cos((1)/(2)*Pi*(z)^(2))-((1)/(2)- FresnelC(z))* sin((1)/(2)*Pi*(z)^(2)) FresnelF[z]=(Divide[1,2]- FresnelS[z])* Cos[Divide[1,2]*Pi*(z)^(2)]-(Divide[1,2]- FresnelC[z])* Sin[Divide[1,2]*Pi*(z)^(2)] Successful Successful - -
7.2.E11 Fresnelg(z)=((1)/(2)- FresnelC(z))* cos((1)/(2)*Pi*(z)^(2))+((1)/(2)- FresnelS(z))* sin((1)/(2)*Pi*(z)^(2)) FresnelG[z]=(Divide[1,2]- FresnelC[z])* Cos[Divide[1,2]*Pi*(z)^(2)]+(Divide[1,2]- FresnelS[z])* Sin[Divide[1,2]*Pi*(z)^(2)] Successful Successful - -
7.4.E1 erf(- z)= - erf(z) Erf[- z]= - Erf[z] Successful Successful - -
7.4.E2 erfc(- z)= 2 - erfc(z) Erfc[- z]= 2 - Erfc[z] Successful Successful - -
7.4.E4 dawson(- z)= - dawson(z) DawsonF[- z]= - DawsonF[z] Successful Successful - -
7.4#Ex1 FresnelC(- z)= - FresnelC(z) FresnelC[- z]= - FresnelC[z] Successful Successful - -
7.4#Ex2 FresnelS(- z)= - FresnelS(z) FresnelS[- z]= - FresnelS[z] Successful Successful - -
7.4#Ex3 FresnelC(I*z)= I*FresnelC(z) FresnelC[I*z]= I*FresnelC[z] Successful Successful - -
7.4#Ex4 FresnelS(I*z)= - I*FresnelS(z) FresnelS[I*z]= - I*FresnelS[z] Successful Successful - -
7.4#Ex5 Fresnelf(I*z)=(1/sqrt(2))* exp((1)/(4)*Pi*I -(1)/(2)*Pi*I*(z)^(2))- I*Fresnelf(z) FresnelF[I*z]=(1/Sqrt[2])* Exp[Divide[1,4]*Pi*I -Divide[1,2]*Pi*I*(z)^(2)]- I*FresnelF[z] Failure Failure Successful Successful
7.4#Ex6 Fresnelg(I*z)=(1/sqrt(2))* exp(-(1)/(4)*Pi*I -(1)/(2)*Pi*I*(z)^(2))+ I*Fresnelg(z) FresnelG[I*z]=(1/Sqrt[2])* Exp[-Divide[1,4]*Pi*I -Divide[1,2]*Pi*I*(z)^(2)]+ I*FresnelG[z] Failure Failure Successful Successful
7.4#Ex7 Fresnelf(- z)=sqrt(2)*cos((1)/(4)*Pi +(1)/(2)*Pi*(z)^(2))- Fresnelf(z) FresnelF[- z]=Sqrt[2]*Cos[Divide[1,4]*Pi +Divide[1,2]*Pi*(z)^(2)]- FresnelF[z] Failure Successful Successful -
7.4#Ex8 Fresnelg(- z)=sqrt(2)*sin((1)/(4)*Pi +(1)/(2)*Pi*(z)^(2))- Fresnelg(z) FresnelG[- z]=Sqrt[2]*Sin[Divide[1,4]*Pi +Divide[1,2]*Pi*(z)^(2)]- FresnelG[z] Failure Failure Successful Successful
7.5.E3 FresnelC(z)=(1)/(2)+ Fresnelf(z)*sin((1)/(2)*Pi*(z)^(2))- Fresnelg(z)*cos((1)/(2)*Pi*(z)^(2)) FresnelC[z]=Divide[1,2]+ FresnelF[z]*Sin[Divide[1,2]*Pi*(z)^(2)]- FresnelG[z]*Cos[Divide[1,2]*Pi*(z)^(2)] Successful Failure - Successful
7.5.E4 FresnelS(z)=(1)/(2)- Fresnelf(z)*cos((1)/(2)*Pi*(z)^(2))- Fresnelg(z)*sin((1)/(2)*Pi*(z)^(2)) FresnelS[z]=Divide[1,2]- FresnelF[z]*Cos[Divide[1,2]*Pi*(z)^(2)]- FresnelG[z]*Sin[Divide[1,2]*Pi*(z)^(2)] Successful Failure - Successful
7.5.E6 exp(+(1)/(2)*Pi*I*(z)^(2))*(Fresnelg(z)+ I*Fresnelf(z))=(1)/(2)*(1 + I)-(FresnelC(z)+ I*FresnelS(z)) Exp[+Divide[1,2]*Pi*I*(z)^(2)]*(FresnelG[z]+ I*FresnelF[z])=Divide[1,2]*(1 + I)-(FresnelC[z]+ I*FresnelS[z]) Failure Failure
Fail
.149314e-2-.173022e-2*I <- {z = 2^(1/2)-I*2^(1/2)}
-.119473e-2+.149314e-2*I <- {z = -2^(1/2)+I*2^(1/2)}
Successful
7.5.E6 exp(-(1)/(2)*Pi*I*(z)^(2))*(Fresnelg(z)- I*Fresnelf(z))=(1)/(2)*(1 - I)-(FresnelC(z)- I*FresnelS(z)) Exp[-Divide[1,2]*Pi*I*(z)^(2)]*(FresnelG[z]- I*FresnelF[z])=Divide[1,2]*(1 - I)-(FresnelC[z]- I*FresnelS[z]) Failure Failure
Fail
.149314e-2+.173022e-2*I <- {z = 2^(1/2)+I*2^(1/2)}
-.119473e-2-.149314e-2*I <- {z = -2^(1/2)-I*2^(1/2)}
Successful
7.5.E8 FresnelC(z)+ I*FresnelS(z)=(1)/(2)*(1 + I)* erf(zeta) FresnelC[z]+ I*FresnelS[z]=Divide[1,2]*(1 + I)* Erf[\[zeta]] Failure Failure
Fail
-.1423151062+.1316106532*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}
.1316106532-.1423151062*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}
1.141922366+.8679966068*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}
.8679966068+1.141922366*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Error
7.5.E8 FresnelC(z)- I*FresnelS(z)=(1)/(2)*(1 - I)* erf(zeta) FresnelC[z]- I*FresnelS[z]=Divide[1,2]*(1 - I)* Erf[\[zeta]] Failure Failure
Fail
66.79933367+67.80964539*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}
66.52540791+67.53571963*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}
67.53571963+66.52540791*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}
67.80964539+66.79933367*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Error
7.5.E10 Fresnelg(z)+ I*Fresnelf(z)=(1)/(2)*(1 + I)* exp((zeta)^(2))*erfc(zeta) FresnelG[z]+ I*FresnelF[z]=Divide[1,2]*(1 + I)* Exp[(\[zeta])^(2)]*Erfc[\[zeta]] Failure Failure
Fail
-.874918896e-1+.8375300635e-1*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}
.8375400635e-1-.874928896e-1*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}
.1946430180+1.537001110*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}
1.537002110+.1946420180*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Error
7.5.E10 Fresnelg(z)- I*Fresnelf(z)=(1)/(2)*(1 - I)* exp((zeta)^(2))*erfc(zeta) FresnelG[z]- I*FresnelF[z]=Divide[1,2]*(1 - I)* Exp[(\[zeta])^(2)]*Erfc[\[zeta]] Failure Failure
Fail
-.1458959936+.662848896e-1*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}
-.3171418896-.1049610064*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}
1.307352110-.2158500180*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}
-.3500698200e-1-1.558209110*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Error
7.6.E1 erf(z)=(2)/(sqrt(Pi))*sum(((- 1)^(n)* (z)^(2*n + 1))/(factorial(n)*(2*n + 1)), n = 0..infinity) Erf[z]=Divide[2,Sqrt[Pi]]*Sum[Divide[(- 1)^(n)* (z)^(2*n + 1),(n)!*(2*n + 1)], {n, 0, Infinity}] Successful Successful - -
7.6.E4 FresnelC(z)= sum(((- 1)^(n)*((1)/(2)*Pi)^(2*n))/(factorial(2*n)*(4*n + 1))*(z)^(4*n + 1), n = 0..infinity) FresnelC[z]= Sum[Divide[(- 1)^(n)*(Divide[1,2]*Pi)^(2*n),(2*n)!*(4*n + 1)]*(z)^(4*n + 1), {n, 0, Infinity}] Successful Successful - -
7.6.E6 FresnelS(z)= sum(((- 1)^(n)*((1)/(2)*Pi)^(2*n + 1))/(factorial(2*n + 1)*(4*n + 3))*(z)^(4*n + 3), n = 0..infinity) FresnelS[z]= Sum[Divide[(- 1)^(n)*(Divide[1,2]*Pi)^(2*n + 1),(2*n + 1)!*(4*n + 3)]*(z)^(4*n + 3), {n, 0, Infinity}] Successful Successful - -
7.6.E8 Error \|Sqrt[1/2 Pi /$2] BesselI[-2*n - 1/2, 2*n]*(z)^(2)- Sqrt[1/2 Pi /$2] BesselI[(-1)^(1-1)*2*n + 1 + 1/2, 2*n + 1]\|\|Sqrt[1/2 Pi /$2] BesselI[-2*n + 1 - 1/2, 2*n + 1]*(z)^(2)), {n, 0, Infinity}] Error Error - -
7.6.E9 Error \|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]*Divide[1,2]*(z)^(2), {n, 0, Infinity}] Error Error - -
7.6.E10 Error FresnelC[z]= z*Sum[SphericalBesselJ[2*n, Divide[1,2]*Pi*(z)^(2)], {n, 0, Infinity}] Error Failure - Skip
7.6.E11 Error FresnelS[z]= z*Sum[SphericalBesselJ[2*n + 1, Divide[1,2]*Pi*(z)^(2)], {n, 0, Infinity}] Error Failure - Skip
7.7.E1 erfc(z)=(2)/(Pi)*exp(- (z)^(2))*int((exp(- (z)^(2)* (t)^(2)))/((t)^(2)+ 1), t = 0..infinity) Erfc[z]=Divide[2,Pi]*Exp[- (z)^(2)]*Integrate[Divide[Exp[- (z)^(2)* (t)^(2)],(t)^(2)+ 1], {t, 0, Infinity}] Successful Failure - Error
7.7.E2 (1)/(Pi*I)*int((exp(- (t)^(2)))/(t - z), t = - infinity..infinity)=(2*z)/(Pi*I)*int((exp(- (t)^(2)))/((t)^(2)- (z)^(2)), t = 0..infinity) Divide[1,Pi*I]*Integrate[Divide[Exp[- (t)^(2)],t - z], {t, - Infinity, Infinity}]=Divide[2*z,Pi*I]*Integrate[Divide[Exp[- (t)^(2)],(t)^(2)- (z)^(2)], {t, 0, Infinity}] Failure Failure Skip Successful
7.7.E3 int(exp(- a*(t)^(2)+ 2*I*z*t), t = 0..infinity)=(1)/(2)*sqrt((Pi)/(a))*exp(- (z)^(2)/ a)+(I)/(sqrt(a))*dawson((z)/(sqrt(a))) Integrate[Exp[- a*(t)^(2)+ 2*I*z*t], {t, 0, Infinity}]=Divide[1,2]*Sqrt[Divide[Pi,a]]*Exp[- (z)^(2)/ a]+Divide[I,Sqrt[a]]*DawsonF[Divide[z,Sqrt[a]]] Failure Successful Skip -
7.7.E4 int((exp(- a*t))/(sqrt(t + (z)^(2))), t = 0..infinity)=sqrt((Pi)/(a))*exp(a*(z)^(2))*erfc(sqrt(a)*z) Integrate[Divide[Exp[- a*t],Sqrt[t + (z)^(2)]], {t, 0, Infinity}]=Sqrt[Divide[Pi,a]]*Exp[a*(z)^(2)]*Erfc[Sqrt[a]*z] Successful Failure - Successful
7.7.E6 int(exp(-(a*(t)^(2)+ 2*b*t + c)), t = x..infinity)=(1)/(2)*sqrt((Pi)/(a))*exp(((b)^(2)- a*c)/ a)*erfc(sqrt(a)*x +(b)/(sqrt(a))) Integrate[Exp[-(a*(t)^(2)+ 2*b*t + c)], {t, x, Infinity}]=Divide[1,2]*Sqrt[Divide[Pi,a]]*Exp[((b)^(2)- a*c)/ a]*Erfc[Sqrt[a]*x +Divide[b,Sqrt[a]]] Failure Failure Skip Successful
7.7.E7 int(exp(- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))), t = x..infinity)=(sqrt(Pi))/(4*a)*(exp(2*a*b)*erfc(a*x +(b/ x))+ exp(- 2*a*b)*erfc(a*x -(b/ x))) Integrate[Exp[- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))], {t, x, Infinity}]=Divide[Sqrt[Pi],4*a]*(Exp[2*a*b]*Erfc[a*x +(b/ x)]+ Exp[- 2*a*b]*Erfc[a*x -(b/ x)]) Failure Failure Skip Error
7.7.E8 int(exp(- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))), t = 0..infinity)=(sqrt(Pi))/(2*a)*exp(- 2*a*b) Integrate[Exp[- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))], {t, 0, Infinity}]=Divide[Sqrt[Pi],2*a]*Exp[- 2*a*b] Successful Failure - Successful
7.7.E9 int(erf(t), t = 0..x)= x*erf(x)+(1)/(sqrt(Pi))*(exp(- (x)^(2))- 1) Integrate[Erf[t], {t, 0, x}]= x*Erf[x]+Divide[1,Sqrt[Pi]]*(Exp[- (x)^(2)]- 1) Successful Successful - -
7.7.E10 Fresnelf(z)=(1)/(Pi*sqrt(2))*int((exp(- Pi*(z)^(2)* t/ 2))/(sqrt(t)*((t)^(2)+ 1)), t = 0..infinity) FresnelF[z]=Divide[1,Pi*Sqrt[2]]*Integrate[Divide[Exp[- Pi*(z)^(2)* t/ 2],Sqrt[t]*((t)^(2)+ 1)], {t, 0, Infinity}] Failure Failure Skip Error
7.7.E11 Fresnelg(z)=(1)/(Pi*sqrt(2))*int((sqrt(t)*exp(- Pi*(z)^(2)* t/ 2))/((t)^(2)+ 1), t = 0..infinity) FresnelG[z]=Divide[1,Pi*Sqrt[2]]*Integrate[Divide[Sqrt[t]*Exp[- Pi*(z)^(2)* t/ 2],(t)^(2)+ 1], {t, 0, Infinity}] Failure Failure Skip Error
7.7.E12 Fresnelg(z)+ I*Fresnelf(z)= exp(- Pi*I*(z)^(2)/ 2)*int(exp(Pi*I*(t)^(2)/ 2), t = z..infinity) FresnelG[z]+ I*FresnelF[z]= Exp[- Pi*I*(z)^(2)/ 2]*Integrate[Exp[Pi*I*(t)^(2)/ 2], {t, z, Infinity}] Failure Failure Skip
Fail
Complex[-0.12449815517713354, 0.12449815517716199] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.12449815517710515, -0.12449815517713354] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
7.7.E13 Fresnelf(z)=((2*Pi)^(- 3/ 2))/(2*Pi*I)*int((zeta)^(- s)* GAMMA(s)*GAMMA(s +(1)/(2))* GAMMA(s +(3)/(4))*GAMMA((1)/(4)- s), s = c - I*infinity..c + I*infinity) FresnelF[z]=Divide[(2*Pi)^(- 3/ 2),2*Pi*I]*Integrate[(\[zeta])^(- s)* Gamma[s]*Gamma[s +Divide[1,2]]* Gamma[s +Divide[3,4]]*Gamma[Divide[1,4]- s], {s, c - I*Infinity, c + I*Infinity}] Failure Failure Skip Error
7.7.E14 Fresnelg(z)=((2*Pi)^(- 3/ 2))/(2*Pi*I)*int((zeta)^(- s)* GAMMA(s)*GAMMA(s +(1)/(2))* GAMMA(s +(1)/(4))*GAMMA((3)/(4)- s), s = c - I*infinity..c + I*infinity) FresnelG[z]=Divide[(2*Pi)^(- 3/ 2),2*Pi*I]*Integrate[(\[zeta])^(- s)* Gamma[s]*Gamma[s +Divide[1,2]]* Gamma[s +Divide[1,4]]*Gamma[Divide[3,4]- s], {s, c - I*Infinity, c + I*Infinity}] Failure Failure Skip Error
7.7.E15 int(exp(- a*t)*cos((t)^(2)), t = 0..infinity)=sqrt((Pi)/(2))*Fresnelf((a)/(sqrt(2*Pi))) Integrate[Exp[- a*t]*Cos[(t)^(2)], {t, 0, Infinity}]=Sqrt[Divide[Pi,2]]*FresnelF[Divide[a,Sqrt[2*Pi]]] Successful Failure - Error
7.7.E16 int(exp(- a*t)*sin((t)^(2)), t = 0..infinity)=sqrt((Pi)/(2))*Fresnelg((a)/(sqrt(2*Pi))) Integrate[Exp[- a*t]*Sin[(t)^(2)], {t, 0, Infinity}]=Sqrt[Divide[Pi,2]]*FresnelG[Divide[a,Sqrt[2*Pi]]] Successful Failure - Error
7.8.E1 (int(exp(- (t)^(2)), t = x..infinity))/(exp(- (x)^(2)))= exp((x)^(2))*int(exp(- (t)^(2)), t = x..infinity) Divide[Integrate[Exp[- (t)^(2)], {t, x, Infinity}],Exp[- (x)^(2)]]= Exp[(x)^(2)]*Integrate[Exp[- (t)^(2)], {t, x, Infinity}] Successful Successful - -
7.8.E5 ((x)^(2))/(2*(x)^(2)+ 1)< =((x)^(2)*(2*(x)^(2)+ 5))/(4*(x)^(4)+ 12*(x)^(2)+ 3) Divide[(x)^(2),2*(x)^(2)+ 1]< =Divide[(x)^(2)*(2*(x)^(2)+ 5),4*(x)^(4)+ 12*(x)^(2)+ 3] Failure Failure Successful Successful
7.8.E5 (2*(x)^(4)+ 9*(x)^(2)+ 4)/(4*(x)^(4)+ 20*(x)^(2)+ 15)<((x)^(2)+ 1)/(2*(x)^(2)+ 3) Divide[2*(x)^(4)+ 9*(x)^(2)+ 4,4*(x)^(4)+ 20*(x)^(2)+ 15]<Divide[(x)^(2)+ 1,2*(x)^(2)+ 3] Failure Failure Skip Successful
7.8.E6 int(exp(a*(t)^(2)), t = 0..x)<(1)/(3*a*x)*(2*exp(a*(x)^(2))+ a*(x)^(2)- 2) Integrate[Exp[a*(t)^(2)], {t, 0, x}]<Divide[1,3*a*x]*(2*Exp[a*(x)^(2)]+ a*(x)^(2)- 2) Error Failure - Successful
7.8.E7 int(exp((t)^(2)), t = 0..x)<(exp((x)^(2))- 1)/(x) Integrate[Exp[(t)^(2)], {t, 0, x}]<Divide[Exp[(x)^(2)]- 1,x] Failure Failure Skip Successful
7.8.E8 erf(x)<sqrt(1 - exp(- 4*(x)^(2)/ Pi)) Erf[x]<Sqrt[1 - Exp[- 4*(x)^(2)/ Pi]] Failure Failure Skip Successful
7.10.E1 diff(erf(z), [z$(n + 1)])=(- 1)^(n)*(2)/(sqrt(Pi))*HermiteH(n, z)*exp(- (z)^(2)) D[Erf[z], {z, n + 1}]=(- 1)^(n)*Divide[2,Sqrt[Pi]]*HermiteH[n, z]*Exp[- (z)^(2)] Failure Failure Skip Successful
7.10#Ex1 diff(Fresnelf(z), z)= - Pi*z*Fresnelg(z) D[FresnelF[z], z]= - Pi*z*FresnelG[z] Successful Successful - -
7.10#Ex2 diff(Fresnelg(z), z)= Pi*z*Fresnelf(z)- 1 D[FresnelG[z], z]= Pi*z*FresnelF[z]- 1 Successful Successful - -
7.11.E1 erf(z)=(1)/(sqrt(Pi))*GAMMA((1)/(2))-GAMMA((1)/(2), (z)^(2)) Erf[z]=Divide[1,Sqrt[Pi]]*Gamma[Divide[1,2], 0, (z)^(2)] Failure Failure
Fail
-.796532174e-2+.2115950078*I <- {z = 2^(1/2)+I*2^(1/2)}
-.796532174e-2-.2115950078*I <- {z = 2^(1/2)-I*2^(1/2)}
-2.028588748+.7594465268*I <- {z = -2^(1/2)-I*2^(1/2)}
-2.028588748-.7594465268*I <- {z = -2^(1/2)+I*2^(1/2)}
Fail
Complex[-2.020623424050978, 0.547851518927081] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.020623424050978, -0.547851518927081] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
7.11.E2 erfc(z)=(1)/(sqrt(Pi))*GAMMA((1)/(2), (z)^(2)) Erfc[z]=Divide[1,Sqrt[Pi]]*Gamma[Divide[1,2], (z)^(2)] Failure Failure
Fail
2.020623426-.5478515190*I <- {z = -2^(1/2)-I*2^(1/2)}
2.020623426+.5478515190*I <- {z = -2^(1/2)+I*2^(1/2)}
Fail
Complex[2.0206234240509775, -0.547851518927081] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[2.0206234240509775, 0.547851518927081] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
7.11.E3 erfc(z)=(z)/(sqrt(Pi))*Ei((1)/(2), (z)^(2)) Erfc[z]=Divide[z,Sqrt[Pi]]*ExpIntegralE[Divide[1,2], (z)^(2)] Failure Failure
Fail
2.000000000-.1e-9*I <- {z = -2^(1/2)-I*2^(1/2)}
2.000000000+.1e-9*I <- {z = -2^(1/2)+I*2^(1/2)}
Fail
Complex[1.9999999999999996, -1.1102230246251565*^-16] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.9999999999999996, 1.1102230246251565*^-16] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
7.11.E4 erf(z)=(2*z)/(sqrt(Pi))*KummerM((1)/(2), (3)/(2), - (z)^(2)) Erf[z]=Divide[2*z,Sqrt[Pi]]*Hypergeometric1F1[Divide[1,2], Divide[3,2], - (z)^(2)] Successful Successful - -
7.11.E4 (2*z)/(sqrt(Pi))*KummerM((1)/(2), (3)/(2), - (z)^(2))=(2*z)/(sqrt(Pi))*exp(- (z)^(2))*KummerM(1, (3)/(2), (z)^(2)) Divide[2*z,Sqrt[Pi]]*Hypergeometric1F1[Divide[1,2], Divide[3,2], - (z)^(2)]=Divide[2*z,Sqrt[Pi]]*Exp[- (z)^(2)]*Hypergeometric1F1[1, Divide[3,2], (z)^(2)] Successful Successful - -
7.11.E5 erfc(z)=(1)/(sqrt(Pi))*exp(- (z)^(2))*KummerU((1)/(2), (1)/(2), (z)^(2)) Erfc[z]=Divide[1,Sqrt[Pi]]*Exp[- (z)^(2)]*HypergeometricU[Divide[1,2], Divide[1,2], (z)^(2)] Failure Failure
Fail
2.020623426-.5478515190*I <- {z = -2^(1/2)-I*2^(1/2)}
2.020623426+.5478515190*I <- {z = -2^(1/2)+I*2^(1/2)}
Fail
Complex[2.0206234240509775, -0.547851518927081] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[2.0206234240509775, 0.547851518927081] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
7.11.E5 (1)/(sqrt(Pi))*exp(- (z)^(2))*KummerU((1)/(2), (1)/(2), (z)^(2))=(z)/(sqrt(Pi))*exp(- (z)^(2))*KummerU(1, (3)/(2), (z)^(2)) Divide[1,Sqrt[Pi]]*Exp[- (z)^(2)]*HypergeometricU[Divide[1,2], Divide[1,2], (z)^(2)]=Divide[z,Sqrt[Pi]]*Exp[- (z)^(2)]*HypergeometricU[1, Divide[3,2], (z)^(2)] Failure Failure
Fail
-.2062342514e-1+.5478515190*I <- {z = -2^(1/2)-I*2^(1/2)}
-.2062342514e-1-.5478515190*I <- {z = -2^(1/2)+I*2^(1/2)}
Fail
Complex[-0.02062342405097809, 0.5478515189270807] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.020623424050978133, -0.5478515189270807] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
7.11.E6 FresnelC(z)+ I*FresnelS(z)= z*KummerM((1)/(2), (3)/(2), (1)/(2)*Pi*I*(z)^(2)) FresnelC[z]+ I*FresnelS[z]= z*Hypergeometric1F1[Divide[1,2], Divide[3,2], Divide[1,2]*Pi*I*(z)^(2)] Failure Successful Successful -
7.11.E6 z*KummerM((1)/(2), (3)/(2), (1)/(2)*Pi*I*(z)^(2))= z*exp(Pi*I*(z)^(2)/ 2)*KummerM(1, (3)/(2), -(1)/(2)*Pi*I*(z)^(2)) z*Hypergeometric1F1[Divide[1,2], Divide[3,2], Divide[1,2]*Pi*I*(z)^(2)]= z*Exp[Pi*I*(z)^(2)/ 2]*Hypergeometric1F1[1, Divide[3,2], -Divide[1,2]*Pi*I*(z)^(2)] Successful Successful - -
7.11.E7 FresnelC(z)= z*hypergeom([(1)/(4)], [(5)/(4),(1)/(2)], -(1)/(16)*(Pi)^(2)* (z)^(4)) FresnelC[z]= z*HypergeometricPFQ[{Divide[1,4]}, {Divide[5,4],Divide[1,2]}, -Divide[1,16]*(Pi)^(2)* (z)^(4)] Successful Successful - -
7.11.E8 FresnelS(z)=(1)/(6)*Pi*(z)^(3)* hypergeom([(3)/(4)], [(7)/(4),(3)/(2)], -(1)/(16)*(Pi)^(2)* (z)^(4)) FresnelS[z]=Divide[1,6]*Pi*(z)^(3)* HypergeometricPFQ[{Divide[3,4]}, {Divide[7,4],Divide[3,2]}, -Divide[1,16]*(Pi)^(2)* (z)^(4)] Successful Successful - -
7.13#Ex4 mu = ln(lambda*sqrt(2*Pi)) \[Mu]= Log[\[Lambda]*Sqrt[2*Pi]] Failure Failure
Fail
-.197872151+.6288153986*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2)}
-.197872151-2.199611725*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2)}
-3.026299275-2.199611725*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = -2^(1/2)-I*2^(1/2)}
-3.026299275+.6288153986*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Fail
Complex[-0.1978721513915227, 0.6288153989756469] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.1978721513915227, -2.199611725770543] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.026299276137713, -2.199611725770543] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.026299276137713, 0.6288153989756469] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
7.13#Ex8 mu = ln(2*lambda*sqrt(2*Pi)) \[Mu]= Log[2*\[Lambda]*Sqrt[2*Pi]] Failure Failure
Fail
-.891019332+.6288153986*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2)}
-.891019332-2.199611725*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2)}
-3.719446456-2.199611725*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = -2^(1/2)-I*2^(1/2)}
-3.719446456+.6288153986*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Fail
Complex[-0.8910193319514683, 0.6288153989756469] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.8910193319514683, -2.199611725770543] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.719446456697659, -2.199611725770543] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.719446456697659, 0.6288153989756469] <- {Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
7.13#Ex12 alpha =(2/ Pi)* ln(Pi*lambda) \[Alpha]=(2/ Pi)* Log[Pi*\[Lambda]] Failure Failure
Fail
.244184683+.9142135621*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2)}
.244184683+1.914213562*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)-I*2^(1/2)}
.244184683+2.914213561*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = -2^(1/2)-I*2^(1/2)}
.244184683-.85786437e-1*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Fail
Complex[0.24418468271597948, 0.9142135623730951] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.24418468271597948, 1.9142135623730951] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.24418468271597948, 2.914213562373095] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.24418468271597948, -0.08578643762690485] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
7.13#Ex14 alpha =(2/ Pi)* ln(Pi*lambda) \[Alpha]=(2/ Pi)* Log[Pi*\[Lambda]] Failure Failure
Fail
.244184683+.9142135621*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2)}
.244184683+1.914213562*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)-I*2^(1/2)}
.244184683+2.914213561*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = -2^(1/2)-I*2^(1/2)}
.244184683-.85786437e-1*I <- {alpha = 2^(1/2)+I*2^(1/2), lambda = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Fail
Complex[0.24418468271597948, 0.9142135623730951] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.24418468271597948, 1.9142135623730951] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.24418468271597948, 2.914213562373095] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.24418468271597948, -0.08578643762690485] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[λ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
7.14.E1 int(exp(2*I*a*t)*erfc(b*t), t = 0..infinity)=(1)/(a*sqrt(Pi))*dawson((a)/(b))+(I)/(2*a)*(1 - exp(-(a/ b)^(2))) Integrate[Exp[2*I*a*t]*Erfc[b*t], {t, 0, Infinity}]=Divide[1,a*Sqrt[Pi]]*DawsonF[Divide[a,b]]+Divide[I,2*a]*(1 - Exp[-(a/ b)^(2)]) Failure Failure Skip Error
7.14.E2 int(exp(- a*t)*erf(b*t), t = 0..infinity)=(1)/(a)*exp((a)^(2)/(4*(b)^(2)))*erfc((a)/(2*b)) Integrate[Exp[- a*t]*Erf[b*t], {t, 0, Infinity}]=Divide[1,a]*Exp[(a)^(2)/(4*(b)^(2))]*Erfc[Divide[a,2*b]] Successful Failure - Error
7.14.E4 int(exp((a - b)* t)*erfc(sqrt(a*t)+sqrt((c)/(t))), t = 0..infinity)=(exp(- 2*(sqrt(a*c)+sqrt(b*c))))/(sqrt(b)*(sqrt(a)+sqrt(b))) Integrate[Exp[(a - b)* t]*Erfc[Sqrt[a*t]+Sqrt[Divide[c,t]]], {t, 0, Infinity}]=Divide[Exp[- 2*(Sqrt[a*c]+Sqrt[b*c])],Sqrt[b]*(Sqrt[a]+Sqrt[b])] Failure Failure Skip Error
7.14.E5 int(exp(- a*t)*FresnelC(t), t = 0..infinity)=(1)/(a)*Fresnelf((a)/(Pi)) Integrate[Exp[- a*t]*FresnelC[t], {t, 0, Infinity}]=Divide[1,a]*FresnelF[Divide[a,Pi]] Failure Failure Skip Successful
7.14.E6 int(exp(- a*t)*FresnelS(t), t = 0..infinity)=(1)/(a)*Fresnelg((a)/(Pi)) Integrate[Exp[- a*t]*FresnelS[t], {t, 0, Infinity}]=Divide[1,a]*FresnelG[Divide[a,Pi]] Failure Failure Skip Successful
7.17#Ex1 Error y = InverseErf[x] Error Failure -
Fail
DirectedInfinity[-1] <- {Rule[x, 1], Rule[y, 1]}
DirectedInfinity[-1] <- {Rule[x, 1], Rule[y, 2]}
DirectedInfinity[-1] <- {Rule[x, 1], Rule[y, 3]}
7.17#Ex2 Error y = InverseErfc[x] Error Failure -
Fail
1.0 <- {Rule[x, 1], Rule[y, 1]}
2.0 <- {Rule[x, 1], Rule[y, 2]}
3.0 <- {Rule[x, 1], Rule[y, 3]}
DirectedInfinity[1] <- {Rule[x, 2], Rule[y, 1]}
... skip entries to safe data
7.18#Ex1 erfc(- 1, z)=(2)/(sqrt(Pi))*exp(- (z)^(2)) I^(- 1)*Erfc[z]=Divide[2,Sqrt[Pi]]*Exp[- (z)^(2)] Successful Failure -
Fail
Complex[1.011483603950918, -0.8436484572858769] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.46363208502383696, 0.8642718813368542] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.46363208502383696, -2.864271881336854] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.011483603950918, -1.1563515427141229] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
7.18#Ex2 erfc(0, z)= erfc(z) I^(0)*Erfc[z]= Erfc[z] Successful Successful - -
7.18.E2 erfc(n, z)= int(erfc(n - 1, t), t = z..infinity) I^(n)*Erfc[z]= Integrate[I^(n - 1)*Erfc[t], {t, z, Infinity}] Failure Failure Skip
Fail
Complex[-0.30711932433427286, -0.06448523556221403] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.06448523556221401, -0.30711932433427286] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.30711932433427286, 0.06448523556221403] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.2407321945928082, 0.04386181151123664] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
7.18.E2 int(erfc(n - 1, t), t = z..infinity)=(2)/(sqrt(Pi))*int(((t - z)^(n))/(factorial(n))*exp(- (t)^(2)), t = z..infinity) Integrate[I^(n - 1)*Erfc[t], {t, z, Infinity}]=Divide[2,Sqrt[Pi]]*Integrate[Divide[(t - z)^(n),(n)!]*Exp[- (t)^(2)], {t, z, Infinity}] Failure Failure Skip
Fail
Complex[-0.06643066657209085, 0.02648998567028575] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.036107850584238765, -0.054264273946754926] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.04191638050136022, 0.039897144071178225] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.03610785058423853, 0.054264273946755606] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
7.18.E3 diff(erfc(n, z), z)= - erfc(n - 1, z) D[I^(n)*Erfc[z], z]= - I^(n - 1)*Erfc[z] Successful Failure -
Fail
Complex[-0.8436484572858769, -1.011483603950918] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.8642718813368542, -0.46363208502383696] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.864271881336854, -0.46363208502383696] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.1563515427141229, -1.011483603950918] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
7.18.E4