Results of Incomplete Gamma and Related Functions
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 8.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{z} = \int_{0}^{z}t^{a-1}e^{-t}\diff{t}} | GAMMA(a)-GAMMA(a, z)= int((t)^(a - 1)* exp(- t), t = 0..z) |
Gamma[a, 0, z]= Integrate[(t)^(a - 1)* Exp[- t], {t, 0, z}] |
Failure | Successful | Skip | - |
| 8.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a}{z} = \int_{z}^{\infty}t^{a-1}e^{-t}\diff{t}} | GAMMA(a, z)= int((t)^(a - 1)* exp(- t), t = z..infinity) |
Gamma[a, z]= Integrate[(t)^(a - 1)* Exp[- t], {t, z, Infinity}] |
Failure | Failure | Skip | Successful |
| 8.2.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{z}+\incGamma@{a}{z} = \EulerGamma@{a}} | GAMMA(a)-GAMMA(a, z)+ GAMMA(a, z)= GAMMA(a) |
Gamma[a, 0, z]+ Gamma[a, z]= Gamma[a] |
Successful | Successful | - | - |
| 8.2#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincGammaP@{a}{z} = \frac{\incgamma@{a}{z}}{\EulerGamma@{a}}} | (GAMMA(a)-GAMMA(a, z))/GAMMA(a)=(GAMMA(a)-GAMMA(a, z))/(GAMMA(a)) |
GammaRegularized[a, 0, z]=Divide[Gamma[a, 0, z],Gamma[a]] |
Successful | Successful | - | - |
| 8.2#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincGammaQ@{a}{z} = \frac{\incGamma@{a}{z}}{\EulerGamma@{a}}} | GAMMA(a, z)/GAMMA(a)=(GAMMA(a, z))/(GAMMA(a)) |
GammaRegularized[a, z]=Divide[Gamma[a, z],Gamma[a]] |
Successful | Successful | - | - |
| 8.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincGammaP@{a}{z}+\normincGammaQ@{a}{z} = 1} | (GAMMA(a)-GAMMA(a, z))/GAMMA(a)+ GAMMA(a, z)/GAMMA(a)= 1 |
GammaRegularized[a, 0, z]+ GammaRegularized[a, z]= 1 |
Successful | Successful | - | - |
| 8.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \scincgamma@{a}{z} = z^{-a}\normincGammaP@{a}{z}} | (z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a)= (z)^(- a)* (GAMMA(a)-GAMMA(a, z))/GAMMA(a) |
Error |
Successful | Error | - | - |
| 8.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{-a}\normincGammaP@{a}{z} = \frac{z^{-a}}{\EulerGamma@{a}}\incgamma@{a}{z}} | (z)^(- a)* (GAMMA(a)-GAMMA(a, z))/GAMMA(a)=((z)^(- a))/(GAMMA(a))*GAMMA(a)-GAMMA(a, z) |
(z)^(- a)* GammaRegularized[a, 0, z]=Divide[(z)^(- a),Gamma[a]]*Gamma[a, 0, z] |
Failure | Successful | Fail .3504429851+.4826856014*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-.4474572306+.2704599710*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}23.62700226+82.69161801*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}3.420707652-13.57627439*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
- |
| 8.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \scincgamma@{a}{z} = \frac{1}{\EulerGamma@{a}}\int_{0}^{1}t^{a-1}e^{-zt}\diff{t}} | (z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a)=(1)/(GAMMA(a))*int((t)^(a - 1)* exp(- z*t), t = 0..1) |
Error |
Failure | Error | Skip | - |
| 8.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{ze^{2\pi mi}} = e^{2\pi mia}\incgamma@{a}{z}} | GAMMA(a)-GAMMA(a, z*exp(2*Pi*m*I))= exp(2*Pi*m*I*a)*GAMMA(a)-GAMMA(a, z) |
Gamma[a, 0, z*Exp[2*Pi*m*I]]= Exp[2*Pi*m*I*a]*Gamma[a, 0, z] |
Failure | Failure | Successful | Successful |
| 8.2.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a}{ze^{2\pi mi}} = e^{2\pi mia}\incGamma@{a}{z}+(1-e^{2\pi mia})\EulerGamma@{a}} | GAMMA(a, z*exp(2*Pi*m*I))= exp(2*Pi*m*I*a)*GAMMA(a, z)+(1 - exp(2*Pi*m*I*a))* GAMMA(a) |
Gamma[a, z*Exp[2*Pi*m*I]]= Exp[2*Pi*m*I*a]*Gamma[a, z]+(1 - Exp[2*Pi*m*I*a])* Gamma[a] |
Failure | Failure | Fail -.2249049111-.4410511843e-1*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}-.2248750758-.4411585330e-1*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}-.2248750795-.4411584875e-1*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}-1.005323136+.3326243216*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 1}... skip entries to safe data |
Fail
Complex[-0.22490491118791595, -0.04410511845656586] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.2248750764783257, -0.044115852492705915] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.22487507925834865, -0.04411584909968558] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.0053231382729926, 0.33262432134470665] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 8.2.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\pi ia}\incGamma@{a}{ze^{\pi i}}-e^{\pi ia}\incGamma@{a}{ze^{-\pi i}} = -\frac{2\pi i}{\EulerGamma@{1-a}}} | exp(- Pi*I*a)*GAMMA(a, z*exp(Pi*I))- exp(Pi*I*a)*GAMMA(a, z*exp(- Pi*I))= -(2*Pi*I)/(GAMMA(1 - a)) |
Exp[- Pi*I*a]*Gamma[a, z*Exp[Pi*I]]- Exp[Pi*I*a]*Gamma[a, z*Exp[- Pi*I]]= -Divide[2*Pi*I,Gamma[1 - a]] |
Failure | Failure | Fail -7167.292469-174.9289096*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}2.16987973+12.77160007*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}8.705606105-17.43270949*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-4.50134822-89.91653387*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-7167.2924809060105, -174.9289096706231] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.169879706441371, 12.771600034859095] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[8.70560609871773, -17.43270953363519] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.501348191090425, -89.91653394957189] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 8.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a}{ze^{+\pi i}} = \EulerGamma@{a}(1-z^{a}e^{+\pi ia}\scincgamma@{a}{-z})} | GAMMA(a, z*exp(+ Pi*I))= GAMMA(a)*(1 - (z)^(a)* exp(+ Pi*I*a)*(- z)^(-(a))*(GAMMA(a)-GAMMA(a, - z))/GAMMA(a)) |
Error |
Failure | Error | Fail 20.46249972+81.80630504*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-1.005323138+.3326243220*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}1095.761010-111.2868863*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-1231.554386+1108.053849*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
- |
| 8.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a}{ze^{-\pi i}} = \EulerGamma@{a}(1-z^{a}e^{-\pi ia}\scincgamma@{a}{-z})} | GAMMA(a, z*exp(- Pi*I))= GAMMA(a)*(1 - (z)^(a)* exp(- Pi*I*a)*(- z)^(-(a))*(GAMMA(a)-GAMMA(a, - z))/GAMMA(a)) |
Error |
Failure | Error | Fail 1095.761010+111.2868863*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-1231.554386-1108.053849*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}20.46249972-81.80630504*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-1.005323138-.3326243220*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}... skip entries to safe data |
- |
| 8.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}+\left(1+\frac{1-a}{z}\right)\deriv{w}{z} = 0} | diff(w, [z$(2)])+(1 +(1 - a)/(z))* diff(w, z)= 0 |
D[w, {z, 2}]+(1 +Divide[1 - a,z])* D[w, z]= 0 |
Successful | Successful | - | - |
| 8.2.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}-\left(1+\frac{1-a}{z}\right)\deriv{w}{z}+\frac{1-a}{z^{2}}w = 0} | diff(w, [z$(2)])-(1 +(1 - a)/(z))* diff(w, z)+(1 - a)/((z)^(2))*w = 0 |
D[w, {z, 2}]-(1 +Divide[1 - a,z])* D[w, z]+Divide[1 - a,(z)^(2)]*w = 0 |
Failure | Failure | Fail -.6464466093-.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}.6464466093+.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-.6464466093-.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}.6464466093+.3535533907*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-0.6464466094067263, -0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.6464466094067263, 0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.6464466094067263, -0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.6464466094067263, 0.35355339059327373] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 8.2.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\deriv[2]{\scincgamma}{z}+(a+1+z)\deriv{\scincgamma}{z}+a\scincgamma = 0} | z*diff((+)^(-(z))*(GAMMA(z)-GAMMA(z, +))/GAMMA(z), [(a + 1 + z)*$(2)])*diff((+)^(-(z))*(GAMMA(z)-GAMMA(z, +))/GAMMA(z), a)*(0)^(-(=))*(GAMMA(=)-GAMMA(=, 0))/GAMMA(=) |
Error |
Error | Error | - | - |
| 8.4.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{\tfrac{1}{2}}{z^{2}} = 2\int_{0}^{z}e^{-t^{2}}\diff{t}} | GAMMA((1)/(2))-GAMMA((1)/(2), (z)^(2))= 2*int(exp(- (t)^(2)), t = 0..z) |
Gamma[Divide[1,2], 0, (z)^(2)]= 2*Integrate[Exp[- (t)^(2)], {t, 0, z}] |
Failure | Failure | Skip | Fail
Complex[3.581461769189045, -0.9710415344467407] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[3.581461769189045, 0.9710415344467407] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 8.4.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\int_{0}^{z}e^{-t^{2}}\diff{t} = \sqrt{\pi}\erf@{z}} | 2*int(exp(- (t)^(2)), t = 0..z)=sqrt(Pi)*erf(z) |
2*Integrate[Exp[- (t)^(2)], {t, 0, z}]=Sqrt[Pi]*Erf[z] |
Successful | Successful | - | - |
| 8.4.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \scincgamma@{a}{0} = \frac{1}{\EulerGamma@{a+1}}} | (0)^(-(a))*(GAMMA(a)-GAMMA(a, 0))/GAMMA(a)=(1)/(GAMMA(a + 1)) |
Error |
Failure | Error | Fail -.6493698774+1.106937485*I <- {a = 2^(1/2)+I*2^(1/2)}-.6493698774-1.106937485*I <- {a = 2^(1/2)-I*2^(1/2)}4.564263782+2.639434666*I <- {a = -2^(1/2)-I*2^(1/2)}4.564263782-2.639434666*I <- {a = -2^(1/2)+I*2^(1/2)} |
- |
| 8.4.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \scincgamma@{\tfrac{1}{2}}{-z^{2}} = \frac{2e^{z^{2}}}{z\sqrt{\pi}}\DawsonsintF@{z}} | (- (z)^(2))^(-((1)/(2)))*(GAMMA((1)/(2))-GAMMA((1)/(2), - (z)^(2)))/GAMMA((1)/(2))=(2*exp((z)^(2)))/(z*sqrt(Pi))*dawson(z) |
Error |
Successful | Error | - | - |
| 8.4.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{0}{z} = \int_{z}^{\infty}t^{-1}e^{-t}\diff{t}} | GAMMA(0, z)= int((t)^(- 1)* exp(- t), t = z..infinity) |
Gamma[0, z]= Integrate[(t)^(- 1)* Exp[- t], {t, z, Infinity}] |
Successful | Failure | - | Successful |
| 8.4.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{z}^{\infty}t^{-1}e^{-t}\diff{t} = \expintE@{z}} | int((t)^(- 1)* exp(- t), t = z..infinity)= Ei(z) |
Integrate[(t)^(- 1)* Exp[- t], {t, z, Infinity}]= -ExpIntegralEi[-(z)] |
Failure | Failure | Skip | Successful |
| 8.4.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{1}{z} = e^{-z}} | GAMMA(1, z)= exp(- z) |
Gamma[1, z]= Exp[- z] |
Successful | Successful | - | - |
| 8.4.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{\tfrac{1}{2}}{z^{2}} = 2\int_{z}^{\infty}e^{-t^{2}}\diff{t}} | GAMMA((1)/(2), (z)^(2))= 2*int(exp(- (t)^(2)), t = z..infinity) |
Gamma[Divide[1,2], (z)^(2)]= 2*Integrate[Exp[- (t)^(2)], {t, z, Infinity}] |
Failure | Failure | Skip | Fail
Complex[-3.581461769189044, 0.9710415344467407] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.581461769189044, -0.9710415344467407] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 8.4.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\int_{z}^{\infty}e^{-t^{2}}\diff{t} = \sqrt{\pi}\erfc@{z}} | 2*int(exp(- (t)^(2)), t = z..infinity)=sqrt(Pi)*erfc(z) |
2*Integrate[Exp[- (t)^(2)], {t, z, Infinity}]=Sqrt[Pi]*Erfc[z] |
Successful | Successful | - | - |
| 8.4.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{n+1}{z} = n!(1-e^{-z}e_{n}(z))} | GAMMA(n + 1)-GAMMA(n + 1, z)= factorial(n)*(1 - exp(- z)*exp(1)[n]*(z)) |
Gamma[n + 1, 0, z]= (n)!*(1 - Exp[- z]*Subscript[E, n]*(z)) |
Failure | Failure | Error | Successful |
| 8.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{n+1}{z} = n!e^{-z}e_{n}(z)} | GAMMA(n + 1, z)= factorial(n)*exp(- z)*exp(1)[n]*(z) |
Gamma[n + 1, z]= (n)!*Exp[- z]*Subscript[E, n]*(z) |
Failure | Failure | Error | Successful |
| 8.4.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincGammaP@{n+1}{z} = 1-e^{-z}e_{n}(z)} | (GAMMA(n + 1)-GAMMA(n + 1, z))/GAMMA(n + 1)= 1 - exp(- z)*exp(1)[n]*(z) |
GammaRegularized[n + 1, 0, z]= 1 - Exp[- z]*Subscript[E, n]*(z) |
Failure | Failure | Error | Successful |
| 8.4.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincGammaQ@{n+1}{z} = e^{-z}e_{n}(z)} | GAMMA(n + 1, z)/GAMMA(n + 1)= exp(- z)*exp(1)[n]*(z) |
GammaRegularized[n + 1, z]= Exp[- z]*Subscript[E, n]*(z) |
Failure | Failure | Error | Successful |
| 8.4.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \scincgamma@{-n}{z} = z^{n}} | (z)^(-(- n))*(GAMMA(- n)-GAMMA(- n, z))/GAMMA(- n)= (z)^(n) |
Error |
Failure | Error | Fail Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)+I*2^(1/2), n = 1}Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)+I*2^(1/2), n = 2}Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)+I*2^(1/2), n = 3}Float(undefined)+Float(undefined)*I <- {z = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
- |
| 8.4.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{1-n}{z} = z^{1-n}\genexpintE{n}@{z}} | GAMMA(1 - n, z)= (z)^(1 - n)* Ei(n, z) |
Gamma[1 - n, z]= (z)^(1 - n)* ExpIntegralE[n, z] |
Successful | Successful | - | - |
| 8.4.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincGammaQ@{n+\tfrac{1}{2}}{z^{2}} = \erfc@{z}+\frac{e^{-z^{2}}}{\sqrt{\pi}}\sum_{k=1}^{n}\frac{z^{2k-1}}{\Pochhammersym{\tfrac{1}{2}}{k}}} | GAMMA(n +(1)/(2), (z)^(2))/GAMMA(n +(1)/(2))= erfc(z)+(exp(- (z)^(2)))/(sqrt(Pi))*sum(((z)^(2*k - 1))/(pochhammer((1)/(2), k)), k = 1..n) |
GammaRegularized[n +Divide[1,2], (z)^(2)]= Erfc[z]+Divide[Exp[- (z)^(2)],Sqrt[Pi]]*Sum[Divide[(z)^(2*k - 1),Pochhammer[Divide[1,2], k]], {k, 1, n}] |
Failure | Failure | Skip | Fail
Complex[-6.522116143801526, 0.8770870118427658] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-7.400077458243353, -11.126893574158686] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[11.80629147935897, -12.531631677265604] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-6.522116143801526, -0.8770870118427658] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 8.4.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{-n}{z} = \frac{(-1)^{n}}{n!}\left(\expintE@{z}-e^{-z}\sum_{k=0}^{n-1}\frac{(-1)^{k}k!}{z^{k+1}}\right)} | GAMMA(- n, z)=((- 1)^(n))/(factorial(n))*(Ei(z)- exp(- z)*sum(((- 1)^(k)* factorial(k))/((z)^(k + 1)), k = 0..n - 1)) |
Gamma[- n, z]=Divide[(- 1)^(n),(n)!]*(-ExpIntegralEi[-(z)]- Exp[- z]*Sum[Divide[(- 1)^(k)* (k)!,(z)^(k + 1)], {k, 0, n - 1}]) |
Failure | Failure | Skip | Fail
Complex[1.3877787807814457*^-17, 3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.734723475976807*^-18, -1.5707963267948966] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.3368086899420177*^-19, 0.5235987755982987] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.3877787807814457*^-17, -3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 8.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{z} = a^{-1}z^{a}e^{-z}\KummerconfhyperM@{1}{1+a}{z}} | GAMMA(a)-GAMMA(a, z)= (a)^(- 1)* (z)^(a)* exp(- z)*KummerM(1, 1 + a, z) |
Gamma[a, 0, z]= (a)^(- 1)* (z)^(a)* Exp[- z]*Hypergeometric1F1[1, 1 + a, z] |
Successful | Successful | - | - |
| 8.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a^{-1}z^{a}e^{-z}\KummerconfhyperM@{1}{1+a}{z} = a^{-1}z^{a}\KummerconfhyperM@{a}{1+a}{-z}} | (a)^(- 1)* (z)^(a)* exp(- z)*KummerM(1, 1 + a, z)= (a)^(- 1)* (z)^(a)* KummerM(a, 1 + a, - z) |
(a)^(- 1)* (z)^(a)* Exp[- z]*Hypergeometric1F1[1, 1 + a, z]= (a)^(- 1)* (z)^(a)* Hypergeometric1F1[a, 1 + a, - z] |
Successful | Successful | - | - |
| 8.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \scincgamma@{a}{z} = e^{-z}\OlverconfhyperM@{1}{1+a}{z}} | (z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a)= exp(- z)*KummerM(1, 1 + a, z)/GAMMA(1 + a) |
Error |
Successful | Error | - | - |
| 8.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-z}\OlverconfhyperM@{1}{1+a}{z} = \OlverconfhyperM@{a}{1+a}{-z}} | exp(- z)*KummerM(1, 1 + a, z)/GAMMA(1 + a)= KummerM(a, 1 + a, - z)/GAMMA(1 + a) |
Exp[- z]*Hypergeometric1F1Regularized[1, 1 + a, z]= Hypergeometric1F1Regularized[a, 1 + a, - z] |
Successful | Successful | - | - |
| 8.5.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a}{z} = e^{-z}\KummerconfhyperU@{1-a}{1-a}{z}} | GAMMA(a, z)= exp(- z)*KummerU(1 - a, 1 - a, z) |
Gamma[a, z]= Exp[- z]*HypergeometricU[1 - a, 1 - a, z] |
Successful | Successful | - | - |
| 8.5.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-z}\KummerconfhyperU@{1-a}{1-a}{z} = z^{a}e^{-z}\KummerconfhyperU@{1}{1+a}{z}} | exp(- z)*KummerU(1 - a, 1 - a, z)= (z)^(a)* exp(- z)*KummerU(1, 1 + a, z) |
Exp[- z]*HypergeometricU[1 - a, 1 - a, z]= (z)^(a)* Exp[- z]*HypergeometricU[1, 1 + a, z] |
Successful | Successful | - | - |
| 8.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{z} = a^{-1}z^{\frac{1}{2}a-\frac{1}{2}}e^{-\frac{1}{2}z}\WhittakerconfhyperM{\frac{1}{2}a-\frac{1}{2}}{\frac{1}{2}a}@{z}} | GAMMA(a)-GAMMA(a, z)= (a)^(- 1)* (z)^((1)/(2)*a -(1)/(2))* exp(-(1)/(2)*z)*WhittakerM((1)/(2)*a -(1)/(2), (1)/(2)*a, z) |
Gamma[a, 0, z]= (a)^(- 1)* (z)^(Divide[1,2]*a -Divide[1,2])* Exp[-Divide[1,2]*z]*WhittakerM[Divide[1,2]*a -Divide[1,2], Divide[1,2]*a, z] |
Successful | Successful | - | - |
| 8.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a}{z} = e^{-\frac{1}{2}z}z^{\frac{1}{2}a-\frac{1}{2}}\WhittakerconfhyperW{\frac{1}{2}a-\frac{1}{2}}{\frac{1}{2}a}@{z}} | GAMMA(a, z)= exp(-(1)/(2)*z)*(z)^((1)/(2)*a -(1)/(2))* WhittakerW((1)/(2)*a -(1)/(2), (1)/(2)*a, z) |
Gamma[a, z]= Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]*a -Divide[1,2])* WhittakerW[Divide[1,2]*a -Divide[1,2], Divide[1,2]*a, z] |
Successful | Successful | - | - |
| 8.6.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{z} = \frac{z^{a}}{\sin@{\pi a}}\int_{0}^{\pi}e^{z\cos@@{t}}\cos@{at+z\sin@@{t}}\diff{t}} | GAMMA(a)-GAMMA(a, z)=((z)^(a))/(sin(Pi*a))*int(exp(z*cos(t))*cos(a*t + z*sin(t)), t = 0..Pi) |
Gamma[a, 0, z]=Divide[(z)^(a),Sin[Pi*a]]*Integrate[Exp[z*Cos[t]]*Cos[a*t + z*Sin[t]], {t, 0, Pi}] |
Failure | Failure | Skip | Error |
| 8.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{z} = z^{\frac{1}{2}a}\int_{0}^{\infty}e^{-t}t^{\frac{1}{2}a-1}\BesselJ{a}@{2\sqrt{zt}}\diff{t}} | GAMMA(a)-GAMMA(a, z)= (z)^((1)/(2)*a)* int(exp(- t)*(t)^((1)/(2)*a - 1)* BesselJ(a, 2*sqrt(z*t)), t = 0..infinity) |
Gamma[a, 0, z]= (z)^(Divide[1,2]*a)* Integrate[Exp[- t]*(t)^(Divide[1,2]*a - 1)* BesselJ[a, 2*Sqrt[z*t]], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 8.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{z} = z^{a}\int_{0}^{\infty}\exp@{-at-ze^{-t}}\diff{t}} | GAMMA(a)-GAMMA(a, z)= (z)^(a)* int(exp(- a*t - z*exp(- t)), t = 0..infinity) |
Gamma[a, 0, z]= (z)^(a)* Integrate[Exp[- a*t - z*Exp[- t]], {t, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 8.6.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a}{z} = \frac{z^{a}e^{-z}}{\EulerGamma@{1-a}}\int_{0}^{\infty}\frac{t^{-a}e^{-t}}{z+t}\diff{t}} | GAMMA(a, z)=((z)^(a)* exp(- z))/(GAMMA(1 - a))*int(((t)^(- a)* exp(- t))/(z + t), t = 0..infinity) |
Gamma[a, z]=Divide[(z)^(a)* Exp[- z],Gamma[1 - a]]*Integrate[Divide[(t)^(- a)* Exp[- t],z + t], {t, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 8.6.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a}{z} = z^{a}e^{-z}\int_{0}^{\infty}\frac{e^{-zt}}{(1+t)^{1-a}}\diff{t}} | GAMMA(a, z)= (z)^(a)* exp(- z)*int((exp(- z*t))/((1 + t)^(1 - a)), t = 0..infinity) |
Gamma[a, z]= (z)^(a)* Exp[- z]*Integrate[Divide[Exp[- z*t],(1 + t)^(1 - a)], {t, 0, Infinity}] |
Successful | Failure | - | Error |
| 8.6.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a}{z} = \frac{2z^{\frac{1}{2}a}e^{-z}}{\EulerGamma@{1-a}}\int_{0}^{\infty}e^{-t}t^{-\frac{1}{2}a}\modBesselK{a}@{2\sqrt{zt}}\diff{t}} | GAMMA(a, z)=(2*(z)^((1)/(2)*a)* exp(- z))/(GAMMA(1 - a))*int(exp(- t)*(t)^(-(1)/(2)*a)* BesselK(a, 2*sqrt(z*t)), t = 0..infinity) |
Gamma[a, z]=Divide[2*(z)^(Divide[1,2]*a)* Exp[- z],Gamma[1 - a]]*Integrate[Exp[- t]*(t)^(-Divide[1,2]*a)* BesselK[a, 2*Sqrt[z*t]], {t, 0, Infinity}] |
Successful | Failure | - | Error |
| 8.6.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a}{z} = z^{a}\int_{0}^{\infty}\exp@{at-ze^{t}}\diff{t}} | GAMMA(a, z)= (z)^(a)* int(exp(a*t - z*exp(t)), t = 0..infinity) |
Gamma[a, z]= (z)^(a)* Integrate[Exp[a*t - z*Exp[t]], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 8.6.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{z} = \frac{-\iunit z^{a}}{2\sin@{\pi a}}\int_{-1}^{(0+)}t^{a-1}e^{zt}\diff{t}} | GAMMA(a)-GAMMA(a, z)=(- I*(z)^(a))/(2*sin(Pi*a))*int((t)^(a - 1)* exp(z*t), t = - 1..(0 +)) |
Gamma[a, 0, z]=Divide[- I*(z)^(a),2*Sin[Pi*a]]*Integrate[(t)^(a - 1)* Exp[z*t], {t, - 1, (0 +)}] |
Error | Failure | - | Error |
| 8.6.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{-a}{ze^{+\pi i}} = \frac{e^{z}e^{-\pi\iunit a}}{\EulerGamma@{1+a}}\int_{0}^{\infty}\frac{t^{a}e^{-zt}}{t-1}\diff{t}} | GAMMA(- a, z*exp(+ Pi*I))=(exp(z)*exp(- Pi*I*a))/(GAMMA(1 + a))*int(((t)^(a)* exp(- z*t))/(t - 1), t = 0..infinity) |
Gamma[- a, z*Exp[+ Pi*I]]=Divide[Exp[z]*Exp[- Pi*I*a],Gamma[1 + a]]*Integrate[Divide[(t)^(a)* Exp[- z*t],t - 1], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 8.6.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{-a}{ze^{-\pi i}} = \frac{e^{z}e^{+\pi\iunit a}}{\EulerGamma@{1+a}}\int_{0}^{\infty}\frac{t^{a}e^{-zt}}{t-1}\diff{t}} | GAMMA(- a, z*exp(- Pi*I))=(exp(z)*exp(+ Pi*I*a))/(GAMMA(1 + a))*int(((t)^(a)* exp(- z*t))/(t - 1), t = 0..infinity) |
Gamma[- a, z*Exp[- Pi*I]]=Divide[Exp[z]*Exp[+ Pi*I*a],Gamma[1 + a]]*Integrate[Divide[(t)^(a)* Exp[- z*t],t - 1], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 8.6.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{z} = \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\frac{\EulerGamma@{s}}{a-s}z^{a-s}\diff{s}} | GAMMA(a)-GAMMA(a, z)=(1)/(2*Pi*I)*int((GAMMA(s))/(a - s)*(z)^(a - s), s = c - I*infinity..c + I*infinity) |
Gamma[a, 0, z]=Divide[1,2*Pi*I]*Integrate[Divide[Gamma[s],a - s]*(z)^(a - s), {s, c - I*Infinity, c + I*Infinity}] |
Failure | Failure | Skip | Error |
| 8.6.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a}{z} = \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{s+a}\frac{z^{-s}}{s}\diff{s}} | GAMMA(a, z)=(1)/(2*Pi*I)*int(GAMMA(s + a)*((z)^(- s))/(s), s = c - I*infinity..c + I*infinity) |
Gamma[a, z]=Divide[1,2*Pi*I]*Integrate[Gamma[s + a]*Divide[(z)^(- s),s], {s, c - I*Infinity, c + I*Infinity}] |
Failure | Failure | Skip | Error |
| 8.6.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a}{z} = -\frac{z^{a-1}e^{-z}}{\EulerGamma@{1-a}}\*\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{s+1-a}\frac{\pi z^{-s}}{\sin@{\pi s}}\diff{s}} | GAMMA(a, z)= -((z)^(a - 1)* exp(- z))/(GAMMA(1 - a))*(1)/(2*Pi*I)*int(GAMMA(s + 1 - a)*(Pi*(z)^(- s))/(sin(Pi*s)), s = c - I*infinity..c + I*infinity) |
Gamma[a, z]= -Divide[(z)^(a - 1)* Exp[- z],Gamma[1 - a]]*Divide[1,2*Pi*I]*Integrate[Gamma[s + 1 - a]*Divide[Pi*(z)^(- s),Sin[Pi*s]], {s, c - I*Infinity, c + I*Infinity}] |
Failure | Failure | Skip | Error |
| 8.7.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \scincgamma@{a}{z} = e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\EulerGamma@{a+k+1}}} | (z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a)= exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..infinity) |
Error |
Successful | Error | - | - |
| 8.7.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\EulerGamma@{a+k+1}} = \frac{1}{\EulerGamma@{a}}\sum_{k=0}^{\infty}\frac{(-z)^{k}}{k!(a+k)}} | exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..infinity)=(1)/(GAMMA(a))*sum(((- z)^(k))/(factorial(k)*(a + k)), k = 0..infinity) |
Exp[- z]*Sum[Divide[(z)^(k),Gamma[a + k + 1]], {k, 0, Infinity}]=Divide[1,Gamma[a]]*Sum[Divide[(- z)^(k),(k)!*(a + k)], {k, 0, Infinity}] |
Successful | Successful | - | - |
| 8.7.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a}{z} = \EulerGamma@{a}-\sum_{k=0}^{\infty}\frac{(-1)^{k}z^{a+k}}{k!(a+k)}} | GAMMA(a, z)= GAMMA(a)- sum(((- 1)^(k)* (z)^(a + k))/(factorial(k)*(a + k)), k = 0..infinity) |
Gamma[a, z]= Gamma[a]- Sum[Divide[(- 1)^(k)* (z)^(a + k),(k)!*(a + k)], {k, 0, Infinity}] |
Successful | Successful | - | - |
| 8.7.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{a}-\sum_{k=0}^{\infty}\frac{(-1)^{k}z^{a+k}}{k!(a+k)} = \EulerGamma@{a}\left(1-z^{a}e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\EulerGamma@{a+k+1}}\right)} | GAMMA(a)- sum(((- 1)^(k)* (z)^(a + k))/(factorial(k)*(a + k)), k = 0..infinity)= GAMMA(a)*(1 - (z)^(a)* exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..infinity)) |
Gamma[a]- Sum[Divide[(- 1)^(k)* (z)^(a + k),(k)!*(a + k)], {k, 0, Infinity}]= Gamma[a]*(1 - (z)^(a)* Exp[- z]*Sum[Divide[(z)^(k),Gamma[a + k + 1]], {k, 0, Infinity}]) |
Successful | Successful | - | - |
| 8.8.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a+1}{z} = a\incgamma@{a}{z}-z^{a}e^{-z}} | GAMMA(a + 1)-GAMMA(a + 1, z)= a*GAMMA(a)-GAMMA(a, z)- (z)^(a)* exp(- z) |
Gamma[a + 1, 0, z]= a*Gamma[a, 0, z]- (z)^(a)* Exp[- z] |
Failure | Successful | Fail .135004907e-1-.2375774782*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}.8693672828+.710002389*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}107.1902160-63.3824277*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-.1657436948-.7422690683*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
- |
| 8.8.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a+1}{z} = a\incGamma@{a}{z}+z^{a}e^{-z}} | GAMMA(a + 1, z)= a*GAMMA(a, z)+ (z)^(a)* exp(- z) |
Gamma[a + 1, z]= a*Gamma[a, z]+ (z)^(a)* Exp[- z] |
Failure | Successful | Successful | - |
| 8.8.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\scincgamma@{a+1}{z} = \scincgamma@{a}{z}-\frac{e^{-z}}{\EulerGamma@{a+1}}} | z*(z)^(-(a + 1))*(GAMMA(a + 1)-GAMMA(a + 1, z))/GAMMA(a + 1)= (z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a)-(exp(- z))/(GAMMA(a + 1)) |
Error |
Failure | Error | Successful | - |
| 8.8.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincGammaP@{a+1}{z} = \normincGammaP@{a}{z}-\frac{z^{a}e^{-z}}{\EulerGamma@{a+1}}} | (GAMMA(a + 1)-GAMMA(a + 1, z))/GAMMA(a + 1)= (GAMMA(a)-GAMMA(a, z))/GAMMA(a)-((z)^(a)* exp(- z))/(GAMMA(a + 1)) |
GammaRegularized[a + 1, 0, z]= GammaRegularized[a, 0, z]-Divide[(z)^(a)* Exp[- z],Gamma[a + 1]] |
Failure | Successful | Successful | - |
| 8.8.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincGammaQ@{a+1}{z} = \normincGammaQ@{a}{z}+\frac{z^{a}e^{-z}}{\EulerGamma@{a+1}}} | GAMMA(a + 1, z)/GAMMA(a + 1)= GAMMA(a, z)/GAMMA(a)+((z)^(a)* exp(- z))/(GAMMA(a + 1)) |
GammaRegularized[a + 1, z]= GammaRegularized[a, z]+Divide[(z)^(a)* Exp[- z],Gamma[a + 1]] |
Failure | Successful | Successful | - |
| 8.8.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a+n}{z} = \Pochhammersym{a}{n}\incgamma@{a}{z}-z^{a}e^{-z}\sum_{k=0}^{n-1}\frac{\EulerGamma@{a+n}}{\EulerGamma@{a+k+1}}z^{k}} | GAMMA(a + n)-GAMMA(a + n, z)= pochhammer(a, n)*GAMMA(a)-GAMMA(a, z)- (z)^(a)* exp(- z)*sum((GAMMA(a + n))/(GAMMA(a + k + 1))*(z)^(k), k = 0..n - 1) |
Gamma[a + n, 0, z]= Pochhammer[a, n]*Gamma[a, 0, z]- (z)^(a)* Exp[- z]*Sum[Divide[Gamma[a + n],Gamma[a + k + 1]]*(z)^(k), {k, 0, n - 1}] |
Failure | Successful | Skip | - |
| 8.8.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{z} = \frac{\EulerGamma@{a}}{\EulerGamma@{a-n}}\incgamma@{a-n}{z}-z^{a-1}e^{-z}\sum_{k=0}^{n-1}\frac{\EulerGamma@{a}}{\EulerGamma@{a-k}}z^{-k}} | GAMMA(a)-GAMMA(a, z)=(GAMMA(a))/(GAMMA(a - n))*GAMMA(a - n)-GAMMA(a - n, z)- (z)^(a - 1)* exp(- z)*sum((GAMMA(a))/(GAMMA(a - k))*(z)^(- k), k = 0..n - 1) |
Gamma[a, 0, z]=Divide[Gamma[a],Gamma[a - n]]*Gamma[a - n, 0, z]- (z)^(a - 1)* Exp[- z]*Sum[Divide[Gamma[a],Gamma[a - k]]*(z)^(- k), {k, 0, n - 1}] |
Failure | Successful | Skip | - |
| 8.8.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a+n}{z} = \Pochhammersym{a}{n}\incGamma@{a}{z}+z^{a}e^{-z}\sum_{k=0}^{n-1}\frac{\EulerGamma@{a+n}}{\EulerGamma@{a+k+1}}z^{k}} | GAMMA(a + n, z)= pochhammer(a, n)*GAMMA(a, z)+ (z)^(a)* exp(- z)*sum((GAMMA(a + n))/(GAMMA(a + k + 1))*(z)^(k), k = 0..n - 1) |
Gamma[a + n, z]= Pochhammer[a, n]*Gamma[a, z]+ (z)^(a)* Exp[- z]*Sum[Divide[Gamma[a + n],Gamma[a + k + 1]]*(z)^(k), {k, 0, n - 1}] |
Successful | Successful | - | - |
| 8.8.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a}{z} = \frac{\EulerGamma@{a}}{\EulerGamma@{a-n}}\incGamma@{a-n}{z}+z^{a-1}e^{-z}\sum_{k=0}^{n-1}\frac{\EulerGamma@{a}}{\EulerGamma@{a-k}}z^{-k}} | GAMMA(a, z)=(GAMMA(a))/(GAMMA(a - n))*GAMMA(a - n, z)+ (z)^(a - 1)* exp(- z)*sum((GAMMA(a))/(GAMMA(a - k))*(z)^(- k), k = 0..n - 1) |
Gamma[a, z]=Divide[Gamma[a],Gamma[a - n]]*Gamma[a - n, z]+ (z)^(a - 1)* Exp[- z]*Sum[Divide[Gamma[a],Gamma[a - k]]*(z)^(- k), {k, 0, n - 1}] |
Failure | Successful | Skip | - |
| 8.8.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincGammaP@{a+n}{z} = \normincGammaP@{a}{z}-z^{a}e^{-z}\sum_{k=0}^{n-1}\frac{z^{k}}{\EulerGamma@{a+k+1}}} | (GAMMA(a + n)-GAMMA(a + n, z))/GAMMA(a + n)= (GAMMA(a)-GAMMA(a, z))/GAMMA(a)- (z)^(a)* exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..n - 1) |
GammaRegularized[a + n, 0, z]= GammaRegularized[a, 0, z]- (z)^(a)* Exp[- z]*Sum[Divide[(z)^(k),Gamma[a + k + 1]], {k, 0, n - 1}] |
Successful | Successful | - | - |
| 8.8.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincGammaQ@{a+n}{z} = \normincGammaQ@{a}{z}+z^{a}e^{-z}\sum_{k=0}^{n-1}\frac{z^{k}}{\EulerGamma@{a+k+1}}} | GAMMA(a + n, z)/GAMMA(a + n)= GAMMA(a, z)/GAMMA(a)+ (z)^(a)* exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..n - 1) |
GammaRegularized[a + n, z]= GammaRegularized[a, z]+ (z)^(a)* Exp[- z]*Sum[Divide[(z)^(k),Gamma[a + k + 1]], {k, 0, n - 1}] |
Successful | Successful | - | - |
| 8.8.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\incgamma@{a}{z} = -\deriv{}{z}\incGamma@{a}{z}} | diff(GAMMA(a)-GAMMA(a, z), z)= - diff(GAMMA(a, z), z) |
D[Gamma[a, 0, z], z]= - D[Gamma[a, z], z] |
Successful | Successful | - | - |
| 8.8.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\deriv{}{z}\incGamma@{a}{z} = z^{a-1}e^{-z}} | - diff(GAMMA(a, z), z)= (z)^(a - 1)* exp(- z) |
- D[Gamma[a, z], z]= (z)^(a - 1)* Exp[- z] |
Successful | Successful | - | - |
| 8.8.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}(z^{-a}\incgamma@{a}{z}) = (-1)^{n}z^{-a-n}\incgamma@{a+n}{z}} | diff((z)^(- a)* GAMMA(a)-GAMMA(a, z), [z$(n)])=(- 1)^(n)* (z)^(- a - n)* GAMMA(a + n)-GAMMA(a + n, z) |
D[(z)^(- a)* Gamma[a, 0, z], {z, n}]=(- 1)^(n)* (z)^(- a - n)* Gamma[a + n, 0, z] |
Failure | Failure | Skip | Skip |
| 8.8.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}(z^{-a}\incGamma@{a}{z}) = (-1)^{n}z^{-a-n}\incGamma@{a+n}{z}} | diff((z)^(- a)* GAMMA(a, z), [z$(n)])=(- 1)^(n)* (z)^(- a - n)* GAMMA(a + n, z) |
D[(z)^(- a)* Gamma[a, z], {z, n}]=(- 1)^(n)* (z)^(- a - n)* Gamma[a + n, z] |
Failure | Failure | Skip | Skip |
| 8.8.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}(e^{z}\incgamma@{a}{z}) = (-1)^{n}\Pochhammersym{1-a}{n}e^{z}\incgamma@{a-n}{z}} | diff(exp(z)*GAMMA(a)-GAMMA(a, z), [z$(n)])=(- 1)^(n)* pochhammer(1 - a, n)*exp(z)*GAMMA(a - n)-GAMMA(a - n, z) |
D[Exp[z]*Gamma[a, 0, z], {z, n}]=(- 1)^(n)* Pochhammer[1 - a, n]*Exp[z]*Gamma[a - n, 0, z] |
Failure | Failure | Skip | Successful |
| 8.8.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}(z^{a}e^{z}\scincgamma@{a}{z}) = z^{a-n}e^{z}\scincgamma@{a-n}{z}} | diff((z)^(a)* exp(z)*(z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a), [z$(n)])= (z)^(a - n)* exp(z)*(z)^(-(a - n))*(GAMMA(a - n)-GAMMA(a - n, z))/GAMMA(a - n) |
Error |
Failure | Error | Skip | - |
| 8.8.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}(e^{z}\incGamma@{a}{z}) = (-1)^{n}\Pochhammersym{1-a}{n}e^{z}\incGamma@{a-n}{z}} | diff(exp(z)*GAMMA(a, z), [z$(n)])=(- 1)^(n)* pochhammer(1 - a, n)*exp(z)*GAMMA(a - n, z) |
D[Exp[z]*Gamma[a, z], {z, n}]=(- 1)^(n)* Pochhammer[1 - a, n]*Exp[z]*Gamma[a - n, z] |
Failure | Failure | Skip | Skip |
| 8.10.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{1-a}e^{x}\incGamma@{a}{x} <= 1} | (x)^(1 - a)* exp(x)*GAMMA(a, x)< = 1 |
(x)^(1 - a)* Exp[x]*Gamma[a, x]< = 1 |
Failure | Failure | Skip | Successful |
| 8.10.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{x} >= \frac{x^{a-1}}{a}(1-e^{-x})} | GAMMA(a)-GAMMA(a, x)> =((x)^(a - 1))/(a)*(1 - exp(- x)) |
Gamma[a, 0, x]> =Divide[(x)^(a - 1),a]*(1 - Exp[- x]) |
Failure | Failure | Skip | Successful |
| 8.10.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{1-a}e^{x}\incGamma@{a}{x} = 1+\frac{a-1}{x}\vartheta} | (x)^(1 - a)* exp(x)*GAMMA(a, x)= 1 +(a - 1)/(x)*vartheta |
(x)^(1 - a)* Exp[x]*Gamma[a, x]= 1 +Divide[a - 1,x]*\[CurlyTheta] |
Failure | Failure | Fail 1.052938223-1.733408016*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 1}.6195824495-.7346525318*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 2}.4531580595-.4544327802*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)+I*2^(1/2), x = 3}-2.947061775-.5618351419*I <- {a = 2^(1/2)+I*2^(1/2), vartheta = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[1.0529382235611282, -1.733408017034722] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.6195824493248067, -0.7346525326366091] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.4531580595377106, -0.4544327806624232] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϑ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.947061776438873, -0.5618351417809119] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϑ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 8.10.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{n} < x^{1-a}e^{x}\incGamma@{a}{x}} | A[n]< (x)^(1 - a)* exp(x)*GAMMA(a, x) |
Subscript[A, n]< (x)^(1 - a)* Exp[x]*Gamma[a, x] |
Failure | Failure | Successful | Successful |
| 8.10.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{1-a}e^{x}\incGamma@{a}{x} < B_{n}} | (x)^(1 - a)* exp(x)*GAMMA(a, x)< B[n] |
(x)^(1 - a)* Exp[x]*Gamma[a, x]< Subscript[B, n] |
Failure | Failure | Successful | Successful |
| 8.10.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle I = \int_{0}^{x}t^{a-1}e^{t}\diff{t}} | I = int((t)^(a - 1)* exp(t), t = 0..x) |
I = Integrate[(t)^(a - 1)* Exp[t], {t, 0, x}] |
Failure | Failure | Skip | Fail
Complex[-2.925303491814363, 1.0] <- {Rule[a, Rational[1, 2]], Rule[x, 1]}Complex[-6.687685525621974, 1.0000000000000002] <- {Rule[a, Rational[1, 2]], Rule[x, 2]}Complex[-14.626171384019093, 1.0000000000000007] <- {Rule[a, Rational[1, 2]], Rule[x, 3]} |
| 8.10.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t^{a-1}e^{t}\diff{t} = \EulerGamma@{a}x^{a}\scincgamma@{a}{-x}} | int((t)^(a - 1)* exp(t), t = 0..x)= GAMMA(a)*(x)^(a)* (- x)^(-(a))*(GAMMA(a)-GAMMA(a, - x))/GAMMA(a) |
Error |
Failure | Error | Skip | - |
| 8.10#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{a} = (\EulerGamma@{1+a})^{1/(a-1)}} | c[a]=(GAMMA(1 + a))^(1/(a - 1)) |
Subscript[c, a]=(Gamma[1 + a])^(1/(a - 1)) |
Failure | Failure | Fail -.342222950+.7512982152*I <- {a = 2^(1/2)+I*2^(1/2), c[a] = 2^(1/2)+I*2^(1/2)}-.342222950-2.077128909*I <- {a = 2^(1/2)+I*2^(1/2), c[a] = 2^(1/2)-I*2^(1/2)}-3.170650074-2.077128909*I <- {a = 2^(1/2)+I*2^(1/2), c[a] = -2^(1/2)-I*2^(1/2)}-3.170650074+.7512982152*I <- {a = 2^(1/2)+I*2^(1/2), c[a] = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Successful |
| 8.10#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d_{a} = (\EulerGamma@{1+a})^{-1/a}} | d[a]=(GAMMA(1 + a))^(- 1/ a) |
Subscript[d, a]=(Gamma[1 + a])^(- 1/ a) |
Failure | Failure | Fail .7353701374+1.747162536*I <- {a = 2^(1/2)+I*2^(1/2), d[a] = 2^(1/2)+I*2^(1/2)}.7353701374-1.081264588*I <- {a = 2^(1/2)+I*2^(1/2), d[a] = 2^(1/2)-I*2^(1/2)}-2.093056987-1.081264588*I <- {a = 2^(1/2)+I*2^(1/2), d[a] = -2^(1/2)-I*2^(1/2)}-2.093056987+1.747162536*I <- {a = 2^(1/2)+I*2^(1/2), d[a] = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Successful |
| 8.10.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{x}{2a}\left(\left(1+\frac{2}{x}\right)^{a}-1\right) < x^{1-a}e^{x}\incGamma@{a}{x}} | (x)/(2*a)*((1 +(2)/(x))^(a)- 1)< (x)^(1 - a)* exp(x)*GAMMA(a, x) |
Divide[x,2*a]*((1 +Divide[2,x])^(a)- 1)< (x)^(1 - a)* Exp[x]*Gamma[a, x] |
Failure | Failure | Successful | Successful |
| 8.10.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{1-a}e^{x}\incGamma@{a}{x} <= \frac{x}{ac_{a}}\left(\left(1+\frac{c_{a}}{x}\right)^{a}-1\right)} | (x)^(1 - a)* exp(x)*GAMMA(a, x)< =(x)/(a*c[a])*((1 +(c[a])/(x))^(a)- 1) |
(x)^(1 - a)* Exp[x]*Gamma[a, x]< =Divide[x,a*Subscript[c, a]]*((1 +Divide[Subscript[c, a],x])^(a)- 1) |
Failure | Failure | Successful | Successful |
| 8.10.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-e^{-\alpha_{a}x})^{a} <= \normincGammaP@{a}{x}} | (1 - exp(- alpha[a]*x))^(a)< = (GAMMA(a)-GAMMA(a, x))/GAMMA(a) |
(1 - Exp[- Subscript[\[Alpha], a]*x])^(a)< = GammaRegularized[a, 0, x] |
Failure | Failure | Successful | Successful |
| 8.10.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincGammaP@{a}{x} <= (1-e^{-\beta_{a}x})^{a}} | (GAMMA(a)-GAMMA(a, x))/GAMMA(a)< =(1 - exp(- beta[a]*x))^(a) |
GammaRegularized[a, 0, x]< =(1 - Exp[- Subscript[\[Beta], a]*x])^(a) |
Failure | Failure | Successful | Successful |
| 8.10.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\incGamma@{n}{n}}{\EulerGamma@{n}} < \frac{1}{2}} | (GAMMA(n, n))/(GAMMA(n))<(1)/(2) |
Divide[Gamma[n, n],Gamma[n]]<Divide[1,2] |
Failure | Failure | Successful | Successful |
| 8.10.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2} < \frac{\incGamma@{n}{n-1}}{\EulerGamma@{n}}} | (1)/(2)<(GAMMA(n, n - 1))/(GAMMA(n)) |
Divide[1,2]<Divide[Gamma[n, n - 1],Gamma[n]] |
Failure | Failure | Successful | Successful |
| 8.11.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incGamma@{a}{z} = z^{a-1}e^{-z}\left(\sum_{k=0}^{n-1}\frac{u_{k}}{z^{k}}+R_{n}(a,z)\right)} | GAMMA(a, z)= (z)^(a - 1)* exp(- z)*(sum((u[k])/((z)^(k)), k = 0..n - 1)+ R[n]*(a , z)) |
Gamma[a, z]= (z)^(a - 1)* Exp[- z]*(Sum[Divide[Subscript[u, k],(z)^(k)], {k, 0, n - 1}]+ Subscript[R, n]*(a , z)) |
Failure | Failure | Skip | Error |
| 8.11.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{z} = z^{a}e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\Pochhammersym{a}{k+1}}} | GAMMA(a)-GAMMA(a, z)= (z)^(a)* exp(- z)*sum(((z)^(k))/(pochhammer(a, k + 1)), k = 0..infinity) |
Gamma[a, 0, z]= (z)^(a)* Exp[- z]*Sum[Divide[(z)^(k),Pochhammer[a, k + 1]], {k, 0, Infinity}] |
Successful | Successful | - | - |
| 8.11.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{n}(x) = \frac{\incgamma@{n+1}{nx}}{(nx)^{n}e^{-nx}}} | S[n]*(x)=(GAMMA(n + 1)-GAMMA(n + 1, n*x))/((n*x)^(n)* exp(- n*x)) |
Subscript[S, n]*(x)=Divide[Gamma[n + 1, 0, n*x],(n*x)^(n)* Exp[- n*x]] |
Failure | Failure | Fail .6959317335+1.414213562*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 1, x = 1}.633899074+2.828427124*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 1, x = 2}-1.119204955+4.242640686*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 1, x = 3}.219685512+1.414213562*I <- {S[n] = 2^(1/2)+I*2^(1/2), n = 2, x = 1}... skip entries to safe data |
Successful |
| 8.12.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincGammaP@{a}{z} = \tfrac{1}{2}\erfc@{-\eta\sqrt{a/2}}-S(a,\eta)} | (GAMMA(a)-GAMMA(a, z))/GAMMA(a)=(1)/(2)*erfc(- eta*sqrt(a/ 2))- S*(a , eta) |
GammaRegularized[a, 0, z]=Divide[1,2]*Erfc[- \[Eta]*Sqrt[a/ 2]]- S*(a , \[Eta]) |
Failure | Failure | Error | Error |
| 8.12.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincGammaQ@{a}{z} = \tfrac{1}{2}\erfc@{\eta\sqrt{a/2}}+S(a,\eta)} | GAMMA(a, z)/GAMMA(a)=(1)/(2)*erfc(eta*sqrt(a/ 2))+ S*(a , eta) |
GammaRegularized[a, z]=Divide[1,2]*Erfc[\[Eta]*Sqrt[a/ 2]]+ S*(a , \[Eta]) |
Failure | Failure | Error | Error |
| 8.12.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{e^{+\pi ia}}{2i\sin@{\pi a}}\normincGammaQ@{-a}{ze^{+\pi i}} = +\tfrac{1}{2}\erfc@{+ i\eta\sqrt{a/2}}-iT(a,\eta)} | (exp(+ Pi*I*a))/(2*I*sin(Pi*a))*GAMMA(- a, z*exp(+ Pi*I))/GAMMA(- a)= +(1)/(2)*erfc(+ I*eta*sqrt(a/ 2))- I*T*(a , eta) |
Divide[Exp[+ Pi*I*a],2*I*Sin[Pi*a]]*GammaRegularized[- a, z*Exp[+ Pi*I]]= +Divide[1,2]*Erfc[+ I*\[Eta]*Sqrt[a/ 2]]- I*T*(a , \[Eta]) |
Failure | Failure | Error | Error |
| 8.12.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{e^{-\pi ia}}{2i\sin@{\pi a}}\normincGammaQ@{-a}{ze^{-\pi i}} = -\tfrac{1}{2}\erfc@{- i\eta\sqrt{a/2}}-iT(a,\eta)} | (exp(- Pi*I*a))/(2*I*sin(Pi*a))*GAMMA(- a, z*exp(- Pi*I))/GAMMA(- a)= -(1)/(2)*erfc(- I*eta*sqrt(a/ 2))- I*T*(a , eta) |
Divide[Exp[- Pi*I*a],2*I*Sin[Pi*a]]*GammaRegularized[- a, z*Exp[- Pi*I]]= -Divide[1,2]*Erfc[- I*\[Eta]*Sqrt[a/ 2]]- I*T*(a , \[Eta]) |
Failure | Failure | Error | Error |
| 8.12#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{a+1}\frac{e^{+\pi ia}}{2\pi i}\incGamma@{-a}{ze^{+\pi i}} = -\tfrac{1}{2}\erfc@{+ i\eta\sqrt{a/2}}+iT(a,\eta)} | GAMMA(a + 1)*(exp(+ Pi*I*a))/(2*Pi*I)*GAMMA(- a, z*exp(+ Pi*I))= -(1)/(2)*erfc(+ I*eta*sqrt(a/ 2))+ I*T*(a , eta) |
Gamma[a + 1]*Divide[Exp[+ Pi*I*a],2*Pi*I]*Gamma[- a, z*Exp[+ Pi*I]]= -Divide[1,2]*Erfc[+ I*\[Eta]*Sqrt[a/ 2]]+ I*T*(a , \[Eta]) |
Failure | Failure | Error | Error |
| 8.12#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{a+1}\frac{e^{-\pi ia}}{2\pi i}\incGamma@{-a}{ze^{-\pi i}} = +\tfrac{1}{2}\erfc@{- i\eta\sqrt{a/2}}+iT(a,\eta)} | GAMMA(a + 1)*(exp(- Pi*I*a))/(2*Pi*I)*GAMMA(- a, z*exp(- Pi*I))= +(1)/(2)*erfc(- I*eta*sqrt(a/ 2))+ I*T*(a , eta) |
Gamma[a + 1]*Divide[Exp[- Pi*I*a],2*Pi*I]*Gamma[- a, z*Exp[- Pi*I]]= +Divide[1,2]*Erfc[- I*\[Eta]*Sqrt[a/ 2]]+ I*T*(a , \[Eta]) |
Failure | Failure | Error | Error |
| 8.12.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{-a}\scincgamma@{-a}{-z} = \cos@{\pi a}-2\sin@{\pi a}\left(\frac{e^{\frac{1}{2}a\eta^{2}}}{\sqrt{\pi}}\DawsonsintF@{\eta\sqrt{a/2}}+T(a,\eta)\right)} | (z)^(- a)* (- z)^(-(- a))*(GAMMA(- a)-GAMMA(- a, - z))/GAMMA(- a)= cos(Pi*a)- 2*sin(Pi*a)*((exp((1)/(2)*a*(eta)^(2)))/(sqrt(Pi))*dawson(eta*sqrt(a/ 2))+ T*(a , eta)) |
Error |
Failure | Error | Error | - |
| 8.12.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{k}(\eta) = \frac{1}{\eta}\deriv{}{\eta}c_{k-1}(\eta)+(-1)^{k}\frac{g_{k}}{\mu}} | c[k]*(eta)=(1)/(eta)*diff(c[k - 1]*(eta), eta)+(- 1)^(k)*(g[k])/(mu) |
Subscript[c, k]*(\[Eta])=Divide[1,\[Eta]]*D[Subscript[c, k - 1]*(\[Eta]), \[Eta]]+(- 1)^(k)*Divide[Subscript[g, k],\[Mu]] |
Failure | Failure | Skip | Skip |
| 8.12#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d(+\chi) = \sqrt{\tfrac{1}{2}\pi}e^{\chi^{2}/2}\erfc@{+\chi/\sqrt{2}}} | d*(+ chi)=sqrt((1)/(2)*Pi)*exp((chi)^(2)/ 2)*erfc(+ chi/sqrt(2)) |
d*(+ \[Chi])=Sqrt[Divide[1,2]*Pi]*Exp[(\[Chi])^(2)/ 2]*Erfc[+ \[Chi]/Sqrt[2]] |
Failure | Failure | Fail -.3819402210+4.260963736*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)+I*2^(1/2)}3.618059777+.2609637385*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)-I*2^(1/2)}-.3819402210-3.739036260*I <- {chi = 2^(1/2)+I*2^(1/2), d = -2^(1/2)-I*2^(1/2)}-4.381940219+.2609637385*I <- {chi = 2^(1/2)+I*2^(1/2), d = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-0.3819402207134648, 4.260963738906431] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.6180597792865354, -0.26096373890643143] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.425065647600777, -6.540234379036898] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.574934352399223, 2.5402343790368977] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 8.12#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d(-\chi) = \sqrt{\tfrac{1}{2}\pi}e^{\chi^{2}/2}\erfc@{-\chi/\sqrt{2}}} | d*(- chi)=sqrt((1)/(2)*Pi)*exp((chi)^(2)/ 2)*erfc(- chi/sqrt(2)) |
d*(- \[Chi])=Sqrt[Divide[1,2]*Pi]*Exp[(\[Chi])^(2)/ 2]*Erfc[- \[Chi]/Sqrt[2]] |
Failure | Failure | Fail 1.425065646-6.540234377*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)+I*2^(1/2)}-2.574934352-2.540234379*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)-I*2^(1/2)}1.425065646+1.459765619*I <- {chi = 2^(1/2)+I*2^(1/2), d = -2^(1/2)-I*2^(1/2)}5.425065644-2.540234379*I <- {chi = 2^(1/2)+I*2^(1/2), d = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.425065647600777, -6.540234379036898] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.574934352399223, 2.5402343790368977] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.3819402207134648, 4.260963738906431] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[3.6180597792865354, -0.26096373890643143] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[χ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 8.12.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincGammaQ@{a}{x} = q} | GAMMA(a, x)/GAMMA(a)= q |
GammaRegularized[a, x]= q |
Failure | Failure | Fail -.6276752047-.7874152397*I <- {a = 2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 1}-1.269609688-.9406490460*I <- {a = 2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 2}-1.440152063-1.201678512*I <- {a = 2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), x = 3}-.6276752047+2.041011884*I <- {a = 2^(1/2)+I*2^(1/2), q = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[-0.6276752046971461, -0.7874152400294763] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[-1.2696096879275383, -0.9406490461902074] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[-1.4401520638257446, -1.2016785120794473] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[-0.6276752046971461, 2.0410118847167142] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}... skip entries to safe data |
| 8.13.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1+a^{-1} < x_{-}(a)} | 1 + (a)^(- 1)< x[-]*(a) |
1 + (a)^(- 1)< Subscript[x, -]*(a) |
Error | Failure | - | Error |
| 8.13.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{-}(a) < \ln@@{|a|}} | x[-]*(a)< ln(abs(a)) |
Subscript[x, -]*(a)< Log[Abs[a]] |
Error | Failure | - | Error |
| 8.14.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-ax}\frac{\incgamma@{b}{x}}{\EulerGamma@{b}}\diff{x} = \frac{(1+a)^{-b}}{a}} | int(exp(- a*x)*(GAMMA(b)-GAMMA(b, x))/(GAMMA(b)), x = 0..infinity)=((1 + a)^(- b))/(a) |
Integrate[Exp[- a*x]*Divide[Gamma[b, 0, x],Gamma[b]], {x, 0, Infinity}]=Divide[(1 + a)^(- b),a] |
Successful | Failure | - | Error |
| 8.14.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-ax}\incGamma@{b}{x}\diff{x} = \EulerGamma@{b}\frac{1-(1+a)^{-b}}{a}} | int(exp(- a*x)*GAMMA(b, x), x = 0..infinity)= GAMMA(b)*(1 -(1 + a)^(- b))/(a) |
Integrate[Exp[- a*x]*Gamma[b, x], {x, 0, Infinity}]= Gamma[b]*Divide[1 -(1 + a)^(- b),a] |
Failure | Failure | Skip | Error |
| 8.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}x^{a-1}\incgamma@{b}{x}\diff{x} = -\frac{\EulerGamma@{a+b}}{a}} | int((x)^(a - 1)* GAMMA(b)-GAMMA(b, x), x = 0..infinity)= -(GAMMA(a + b))/(a) |
Integrate[(x)^(a - 1)* Gamma[b, 0, x], {x, 0, Infinity}]= -Divide[Gamma[a + b],a] |
Failure | Failure | Skip | Error |
| 8.14.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}x^{a-1}\incGamma@{b}{x}\diff{x} = \frac{\EulerGamma@{a+b}}{a}} | int((x)^(a - 1)* GAMMA(b, x), x = 0..infinity)=(GAMMA(a + b))/(a) |
Integrate[(x)^(a - 1)* Gamma[b, x], {x, 0, Infinity}]=Divide[Gamma[a + b],a] |
Successful | Failure | - | Skip |
| 8.14.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}x^{a-1}e^{-sx}\incgamma@{b}{x}\diff{x} = \frac{\EulerGamma@{a+b}}{b(1+s)^{a+b}}\*\hyperF@{1}{a+b}{1+b}{1/(1+s)}} | int((x)^(a - 1)* exp(- s*x)*GAMMA(b)-GAMMA(b, x), x = 0..infinity)=(GAMMA(a + b))/(b*(1 + s)^(a + b))* hypergeom([1, a + b], [1 + b], 1/(1 + s)) |
Integrate[(x)^(a - 1)* Exp[- s*x]*Gamma[b, 0, x], {x, 0, Infinity}]=Divide[Gamma[a + b],b*(1 + s)^(a + b)]* Hypergeometric2F1[1, a + b, 1 + b, 1/(1 + s)] |
Failure | Failure | Skip | Error |
| 8.14.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}x^{a-1}e^{-sx}\incGamma@{b}{x}\diff{x} = \frac{\EulerGamma@{a+b}}{a(1+s)^{a+b}}\*\hyperF@{1}{a+b}{1+a}{s/(1+s)}} | int((x)^(a - 1)* exp(- s*x)*GAMMA(b, x), x = 0..infinity)=(GAMMA(a + b))/(a*(1 + s)^(a + b))* hypergeom([1, a + b], [1 + a], s/(1 + s)) |
Integrate[(x)^(a - 1)* Exp[- s*x]*Gamma[b, x], {x, 0, Infinity}]=Divide[Gamma[a + b],a*(1 + s)^(a + b)]* Hypergeometric2F1[1, a + b, 1 + a, s/(1 + s)] |
Failure | Failure | Skip | Error |
| 8.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{\lambda x} = \lambda^{a}\sum_{k=0}^{\infty}\incgamma@{a+k}{x}\frac{(1-\lambda)^{k}}{k!}} | GAMMA(a)-GAMMA(a, lambda*x)= (lambda)^(a)* sum(GAMMA(a + k)-GAMMA(a + k, x)*((1 - lambda)^(k))/(factorial(k)), k = 0..infinity) |
Gamma[a, 0, \[Lambda]*x]= (\[Lambda])^(a)* Sum[Gamma[a + k, 0, x]*Divide[(1 - \[Lambda])^(k),(k)!], {k, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 8.17.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incBeta{x}@{a}{b} = \int_{0}^{x}t^{a-1}(1-t)^{b-1}\diff{t}} | int(t^(a-1)*(1-t)^(b-1), t = 0 .. x)= int((t)^(a - 1)*(1 - t)^(b - 1), t = 0..x) |
Beta[x, a, b]= Integrate[(t)^(a - 1)*(1 - t)^(b - 1), {t, 0, x}] |
Successful | Failure | - | Skip |
| 8.17.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincBetaI{x}@{a}{b} = \incBeta{x}@{a}{b}/\EulerBeta@{a}{b}} | Error |
BetaRegularized[x, a, b]= Beta[x, a, b]/ Beta[a, b] |
Error | Successful | - | - |
| 8.17.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerBeta@{a}{b} = \frac{\EulerGamma@{a}\EulerGamma@{b}}{\EulerGamma@{a+b}}} | Beta(a, b)=(GAMMA(a)*GAMMA(b))/(GAMMA(a + b)) |
Beta[a, b]=Divide[Gamma[a]*Gamma[b],Gamma[a + b]] |
Failure | Successful | Error | - |
| 8.17.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincBetaI{x}@{a}{b} = 1-\normincBetaI{1-x}@{b}{a}} | Error |
BetaRegularized[x, a, b]= 1 - BetaRegularized[1 - x, b, a] |
Error | Failure | - | Fail
DirectedInfinity[] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}DirectedInfinity[] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}DirectedInfinity[] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}DirectedInfinity[] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}... skip entries to safe data |
| 8.17.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincBetaI{x}@{m}{n-m+1} = \sum_{j=m}^{n}\binom{n}{j}x^{j}(1-x)^{n-j}} | Error |
BetaRegularized[x, m, n - m + 1]= Sum[Binomial[n,j]*(x)^(j)*(1 - x)^(n - j), {j, m, n}] |
Error | Failure | - | Successful |
| 8.17.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincBetaI{x}@{a}{a} = \tfrac{1}{2}\normincBetaI{4x(1-x)}@{a}{\tfrac{1}{2}}} | Error |
BetaRegularized[x, a, a]=Divide[1,2]*BetaRegularized[4*x*(1 - x), a, Divide[1,2]] |
Error | Failure | - | Successful |
| 8.17.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incBeta{x}@{a}{b} = \frac{x^{a}}{a}\hyperF@{a}{1-b}{a+1}{x}} | int(t^(a-1)*(1-t)^(b-1), t = 0 .. x)=((x)^(a))/(a)*hypergeom([a, 1 - b], [a + 1], x) |
Beta[x, a, b]=Divide[(x)^(a),a]*Hypergeometric2F1[a, 1 - b, a + 1, x] |
Failure | Successful | Skip | - |
| 8.17.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incBeta{x}@{a}{b} = \frac{x^{a}(1-x)^{b}}{a}\hyperF@{a+b}{1}{a+1}{x}} | int(t^(a-1)*(1-t)^(b-1), t = 0 .. x)=((x)^(a)*(1 - x)^(b))/(a)*hypergeom([a + b, 1], [a + 1], x) |
Beta[x, a, b]=Divide[(x)^(a)*(1 - x)^(b),a]*Hypergeometric2F1[a + b, 1, a + 1, x] |
Failure | Successful | Skip | - |
| 8.17.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incBeta{x}@{a}{b} = \frac{x^{a}(1-x)^{b-1}}{a}\hyperF@@{1}{1-b}{a+1}{\frac{x}{x-1}}} | int(t^(a-1)*(1-t)^(b-1), t = 0 .. x)=((x)^(a)*(1 - x)^(b - 1))/(a)*hypergeom([1, 1 - b], [a + 1], (x)/(x - 1)) |
Beta[x, a, b]=Divide[(x)^(a)*(1 - x)^(b - 1),a]*Hypergeometric2F1[1, 1 - b, a + 1, Divide[x,x - 1]] |
Failure | Failure | Skip | Fail
Complex[-0.27132901967319506, -0.2500814455005845] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[-0.27137899275582306, -0.250091870275464] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[-0.27137899275582306, -0.250091870275464] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[0.08838841600311584, 0.0] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}... skip entries to safe data |
| 8.17.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincBetaI{x}@{a}{b} = \frac{x^{a}(1-x)^{b}}{2\pi i}\int_{c-i\infty}^{c+i\infty}s^{-a}(1-s)^{-b}\frac{\diff{s}}{s-x}} | Error |
BetaRegularized[x, a, b]=Divide[(x)^(a)*(1 - x)^(b),2*Pi*I]*Integrate[(s)^(- a)*(1 - s)^(- b)*Divide[1,s - x], {s, c - I*Infinity, c + I*Infinity}] |
Error | Failure | - | Error |
| 8.17.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (a+b)\normincBetaI{x}@{a}{b} = a\normincBetaI{x}@{a+1}{b}+b\normincBetaI{x}@{a}{b+1}} | Error |
(a + b)* BetaRegularized[x, a, b]= a*BetaRegularized[x, a + 1, b]+ b*BetaRegularized[x, a, b + 1] |
Error | Successful | - | - |
| 8.17.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (a+bx)\normincBetaI{x}@{a}{b} = xb\normincBetaI{x}@{a-1}{b+1}+a\normincBetaI{x}@{a+1}{b}} | Error |
(a + b*x)* BetaRegularized[x, a, b]= x*b*BetaRegularized[x, a - 1, b + 1]+ a*BetaRegularized[x, a + 1, b] |
Error | Successful | - | - |
| 8.17.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a\normincBetaI{x}@{a+1}{b} = (a+cx)\normincBetaI{x}@{a}{b}-cx\normincBetaI{x}@{a-1}{b}} | Error |
a*BetaRegularized[x, a + 1, b]=(a + c*x)* BetaRegularized[x, a, b]- c*x*BetaRegularized[x, a - 1, b] |
Error | Failure | - | Skip |
| 8.17.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincBetaI{x}@{m}{n} = (1-x)^{n}\sum_{j=m}^{\infty}\binom{n+j-1}{j}x^{j}} | Error |
BetaRegularized[x, m, n]=(1 - x)^(n)* Sum[Binomial[n + j - 1,j]*(x)^(j), {j, m, Infinity}] |
Error | Failure | - | Successful |
| 8.18.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \xi = -\ln@@{x}} | xi = - ln(x) |
\[Xi]= - Log[x] |
Failure | Failure | Fail 1.414213562+1.414213562*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1}2.107360743+1.414213562*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2}2.512825851+1.414213562*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3}1.414213562-1.414213562*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.1073607429330403, 1.4142135623730951] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.512825851041205, 1.4142135623730951] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 8.18#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle F_{0} = a^{-b}\normincGammaQ@{b}{a\xi}} | F[0]= (a)^(- b)* GAMMA(b, a*xi)/GAMMA(b) |
Subscript[F, 0]= (a)^(- b)* GammaRegularized[b, a*\[Xi]] |
Failure | Failure | Fail 2.106630597+.9392389431*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)+I*2^(1/2)}2.106630597-1.889188181*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = 2^(1/2)-I*2^(1/2)}-.7217965272-1.889188181*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)-I*2^(1/2)}-.7217965272+.9392389431*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), F[0] = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Skip |
| 8.18#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle F_{1} = \frac{b-a\xi}{a}F_{0}+\frac{\xi^{b}e^{-a\xi}}{a\EulerGamma@{b}}} | F[1]=(b - a*xi)/(a)*F[0]+((xi)^(b)* exp(- a*xi))/(a*GAMMA(b)) |
Subscript[F, 1]=Divide[b - a*\[Xi],a]*Subscript[F, 0]+Divide[(\[Xi])^(b)* Exp[- a*\[Xi]],a*Gamma[b]] |
Failure | Failure | Skip | Skip |
| 8.18.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}\eta^{2} = x_{0}\ln@{\frac{x}{x_{0}}}+(1-x_{0})\ln@{\frac{1-x}{1-x_{0}}}} | -(1)/(2)*(eta)^(2)= x[0]*ln((x)/(x[0]))+(1 - x[0])* ln((1 - x)/(1 - x[0])) |
-Divide[1,2]*(\[Eta])^(2)= Subscript[x, 0]*Log[Divide[x,Subscript[x, 0]]]+(1 - Subscript[x, 0])* Log[Divide[1 - x,1 - Subscript[x, 0]]] |
Failure | Failure | Fail Float(undefined)-Float(infinity)*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 1}.547175857-1.970232147*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 2}.260872566-1.563388258*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)+I*2^(1/2), x = 3}Float(undefined)+Float(infinity)*I <- {eta = 2^(1/2)+I*2^(1/2), x[0] = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Successful |
| 8.18.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu\ln@@{\zeta}-\zeta = \ln@@{x}+\mu\ln@{1-x}+(1+\mu)\ln@{1+\mu}-\mu} | mu*ln(zeta)- zeta = ln(x)+ mu*ln(1 - x)+(1 + mu)* ln(1 + mu)- mu |
\[Mu]*Log[\[zeta]]- \[zeta]= Log[x]+ \[Mu]*Log[1 - x]+(1 + \[Mu])* Log[1 + \[Mu]]- \[Mu] |
Failure | Failure | Fail Float(infinity)+Float(infinity)*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 1}1.884730882-5.086259752*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 2}.499007630-6.066517895*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 3}Float(infinity)+Float(infinity)*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Error |
| 8.18.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincBetaI{x}@{a}{b} = p} | Error |
BetaRegularized[x, a, b]= p |
Error | Failure | - | Successful |
| 8.19.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genexpintE{p}@{z} = z^{p-1}\incGamma@{1-p}{z}} | Ei(p, z)= (z)^(p - 1)* GAMMA(1 - p, z) |
ExpIntegralE[p, z]= (z)^(p - 1)* Gamma[1 - p, z] |
Successful | Successful | - | - |
| 8.19.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genexpintE{p}@{z} = z^{p-1}\int_{z}^{\infty}\frac{e^{-t}}{t^{p}}\diff{t}} | Ei(p, z)= (z)^(p - 1)* int((exp(- t))/((t)^(p)), t = z..infinity) |
ExpIntegralE[p, z]= (z)^(p - 1)* Integrate[Divide[Exp[- t],(t)^(p)], {t, z, Infinity}] |
Successful | Failure | - | Skip |
| 8.19.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genexpintE{p}@{z} = \int_{1}^{\infty}\frac{e^{-zt}}{t^{p}}\diff{t}} | Ei(p, z)= int((exp(- z*t))/((t)^(p)), t = 1..infinity) |
ExpIntegralE[p, z]= Integrate[Divide[Exp[- z*t],(t)^(p)], {t, 1, Infinity}] |
Successful | Failure | - | Error |
| 8.19.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genexpintE{p}@{z} = \frac{z^{p-1}e^{-z}}{\EulerGamma@{p}}\int_{0}^{\infty}\frac{t^{p-1}e^{-zt}}{1+t}\diff{t}} | Ei(p, z)=((z)^(p - 1)* exp(- z))/(GAMMA(p))*int(((t)^(p - 1)* exp(- z*t))/(1 + t), t = 0..infinity) |
ExpIntegralE[p, z]=Divide[(z)^(p - 1)* Exp[- z],Gamma[p]]*Integrate[Divide[(t)^(p - 1)* Exp[- z*t],1 + t], {t, 0, Infinity}] |
Successful | Failure | - | Error |
| 8.19.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genexpintE{0}@{z} = z^{-1}e^{-z}} | Ei(0, z)= (z)^(- 1)* exp(- z) |
ExpIntegralE[0, z]= (z)^(- 1)* Exp[- z] |
Successful | Failure | - | Successful |
| 8.19.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genexpintE{p}@{0} = \frac{1}{p-1}} | Ei(p, 0)=(1)/(p - 1) |
ExpIntegralE[p, 0]=Divide[1,p - 1] |
Successful | Successful | - | - |
| 8.19.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genexpintE{n}@{z} = \frac{(-z)^{n-1}}{(n-1)!}\expintE@{z}+\frac{e^{-z}}{(n-1)!}\sum_{k=0}^{n-2}(n-k-2)!(-z)^{k}} | Ei(n, z)=((- z)^(n - 1))/(factorial(n - 1))*Ei(z)+(exp(- z))/(factorial(n - 1))*sum(factorial(n - k - 2)*(- z)^(k), k = 0..n - 2) |
ExpIntegralE[n, z]=Divide[(- z)^(n - 1),(n - 1)!]*-ExpIntegralEi[-(z)]+Divide[Exp[- z],(n - 1)!]*Sum[(n - k - 2)!*(- z)^(k), {k, 0, n - 2}] |
Failure | Failure | Skip | Fail
Complex[0.0, -3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.442882938158367, 4.442882938158366] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.283185307179586, 0.0] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, 3.141592653589793] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 8.19.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genexpintE{n}@{z} = \frac{(-1)^{n}z^{n-1}}{(n-1)!}\ln@@{z}+\frac{e^{-z}}{(n-1)!}\sum_{k=1}^{n-1}(-z)^{k-1}\EulerGamma@{n-k}+\frac{e^{-z}(-z)^{n-1}}{(n-1)!}\sum_{k=0}^{\infty}\frac{z^{k}}{k!}\digamma@{k+1}} | Ei(n, z)=((- 1)^(n)* (z)^(n - 1))/(factorial(n - 1))*ln(z)+(exp(- z))/(factorial(n - 1))*sum((- z)^(k - 1)* GAMMA(n - k), k = 1..n - 1)+(exp(- z)*(- z)^(n - 1))/(factorial(n - 1))*sum(((z)^(k))/(factorial(k))*Psi(k + 1), k = 0..infinity) |
ExpIntegralE[n, z]=Divide[(- 1)^(n)* (z)^(n - 1),(n - 1)!]*Log[z]+Divide[Exp[- z],(n - 1)!]*Sum[(- z)^(k - 1)* Gamma[n - k], {k, 1, n - 1}]+Divide[Exp[- z]*(- z)^(n - 1),(n - 1)!]*Sum[Divide[(z)^(k),(k)!]*PolyGamma[k + 1], {k, 0, Infinity}] |
Error | Failure | - | Successful |
| 8.19.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genexpintE{p}@{z} = z^{p-1}\EulerGamma@{1-p}-\sum_{k=0}^{\infty}\frac{(-z)^{k}}{k!(1-p+k)}} | Ei(p, z)= (z)^(p - 1)* GAMMA(1 - p)- sum(((- z)^(k))/(factorial(k)*(1 - p + k)), k = 0..infinity) |
ExpIntegralE[p, z]= (z)^(p - 1)* Gamma[1 - p]- Sum[Divide[(- z)^(k),(k)!*(1 - p + k)], {k, 0, Infinity}] |
Successful | Successful | - | - |
| 8.19.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genexpintE{p}@{z} = \EulerGamma@{1-p}\left(z^{p-1}-e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\EulerGamma@{2-p+k}}\right)} | Ei(p, z)= GAMMA(1 - p)*((z)^(p - 1)- exp(- z)*sum(((z)^(k))/(GAMMA(2 - p + k)), k = 0..infinity)) |
ExpIntegralE[p, z]= Gamma[1 - p]*((z)^(p - 1)- Exp[- z]*Sum[Divide[(z)^(k),Gamma[2 - p + k]], {k, 0, Infinity}]) |
Successful | Successful | - | - |
| 8.19.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p\genexpintE{p+1}@{z}+z\genexpintE{p}@{z} = e^{-z}} | p*Ei(p + 1, z)+ z*Ei(p, z)= exp(- z) |
p*ExpIntegralE[p + 1, z]+ z*ExpIntegralE[p, z]= Exp[- z] |
Successful | Successful | - | - |
| 8.19.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\genexpintE{p}@{z} = -\genexpintE{p-1}@{z}} | diff(Ei(p, z), z)= - Ei(p - 1, z) |
D[ExpIntegralE[p, z], z]= - ExpIntegralE[p - 1, z] |
Successful | Successful | - | - |
| 8.19.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}(e^{z}\genexpintE{p}@{z}) = e^{z}\genexpintE{p}@{z}\left(1+\frac{p-1}{z}\right)-\frac{1}{z}} | diff(exp(z)*Ei(p, z), z)= exp(z)*Ei(p, z)*(1 +(p - 1)/(z))-(1)/(z) |
D[Exp[z]*ExpIntegralE[p, z], z]= Exp[z]*ExpIntegralE[p, z]*(1 +Divide[p - 1,z])-Divide[1,z] |
Successful | Successful | - | - |
| 8.19.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[j]{\genexpintE{p}@{z}}{p} = (-1)^{j}\int_{1}^{\infty}(\ln@@{t})^{j}t^{-p}e^{-zt}\diff{t}} | diff(Ei(p, z), [p$(j)])=(- 1)^(j)* int((ln(t))^(j)* (t)^(- p)* exp(- z*t), t = 1..infinity) |
D[ExpIntegralE[p, z], {p, j}]=(- 1)^(j)* Integrate[(Log[t])^(j)* (t)^(- p)* Exp[- z*t], {t, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 8.19.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genexpintE{p}@{z} = z^{p-1}e^{-z}\KummerconfhyperU@{p}{p}{z}} | Ei(p, z)= (z)^(p - 1)* exp(- z)*KummerU(p, p, z) |
ExpIntegralE[p, z]= (z)^(p - 1)* Exp[- z]*HypergeometricU[p, p, z] |
Successful | Successful | - | - |
| 8.19.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{n-1}{n}\genexpintE{n}@{x} < \genexpintE{n+1}@{x}} | (n - 1)/(n)*Ei(n, x)< Ei(n + 1, x) |
Divide[n - 1,n]*ExpIntegralE[n, x]< ExpIntegralE[n + 1, x] |
Failure | Failure | Successful | Successful |
| 8.19.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genexpintE{n+1}@{x} < \genexpintE{n}@{x}} | Ei(n + 1, x)< Ei(n, x) |
ExpIntegralE[n + 1, x]< ExpIntegralE[n, x] |
Failure | Failure | Successful | Successful |
| 8.19.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\genexpintE{n}@{x}\right)^{2} < \genexpintE{n-1}@{x}\genexpintE{n+1}@{x}} | (Ei(n, x))^(2)< Ei(n - 1, x)*Ei(n + 1, x) |
(ExpIntegralE[n, x])^(2)< ExpIntegralE[n - 1, x]*ExpIntegralE[n + 1, x] |
Failure | Failure | Successful | Successful |
| 8.19.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{x+n} < e^{x}\genexpintE{n}@{x}} | (1)/(x + n)< exp(x)*Ei(n, x) |
Divide[1,x + n]< Exp[x]*ExpIntegralE[n, x] |
Failure | Failure | Successful | Successful |
| 8.19.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{x}\genexpintE{n}@{x} <= \frac{1}{x+n-1}} | exp(x)*Ei(n, x)< =(1)/(x + n - 1) |
Exp[x]*ExpIntegralE[n, x]< =Divide[1,x + n - 1] |
Failure | Failure | Successful | Successful |
| 8.19.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{x}\frac{\genexpintE{n}@{x}}{\genexpintE{n-1}@{x}} > 0} | diff((Ei(n, x))/(Ei(n - 1, x)), x)> 0 |
D[Divide[ExpIntegralE[n, x],ExpIntegralE[n - 1, x]], x]> 0 |
Failure | Failure | Successful | Successful |
| 8.19.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{z}^{\infty}\genexpintE{p-1}@{t}\diff{t} = \genexpintE{p}@{z}} | int(Ei(p - 1, t), t = z..infinity)= Ei(p, z) |
Integrate[ExpIntegralE[p - 1, t], {t, z, Infinity}]= ExpIntegralE[p, z] |
Failure | Failure | Skip | Successful |
| 8.19.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\genexpintE{n}@{t}\diff{t} = \frac{(-1)^{n-1}}{a^{n}}\left(\ln@{1+a}+\sum_{k=1}^{n-1}\frac{(-1)^{k}a^{k}}{k}\right)} | int(exp(- a*t)*Ei(n, t), t = 0..infinity)=((- 1)^(n - 1))/((a)^(n))*(ln(1 + a)+ sum(((- 1)^(k)* (a)^(k))/(k), k = 1..n - 1)) |
Integrate[Exp[- a*t]*ExpIntegralE[n, t], {t, 0, Infinity}]=Divide[(- 1)^(n - 1),(a)^(n)]*(Log[1 + a]+ Sum[Divide[(- 1)^(k)* (a)^(k),k], {k, 1, n - 1}]) |
Failure | Failure | Skip | Successful |
| 8.19.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}t^{b-1}\genexpintE{p}@{t}\diff{t} = \frac{\EulerGamma@{b}(1+a)^{-b}}{p+b-1}\*\hyperF@{1}{b}{p+b}{a/(1+a)}} | int(exp(- a*t)*(t)^(b - 1)* Ei(p, t), t = 0..infinity)=(GAMMA(b)*(1 + a)^(- b))/(p + b - 1)* hypergeom([1, b], [p + b], a/(1 + a)) |
Integrate[Exp[- a*t]*(t)^(b - 1)* ExpIntegralE[p, t], {t, 0, Infinity}]=Divide[Gamma[b]*(1 + a)^(- b),p + b - 1]* Hypergeometric2F1[1, b, p + b, a/(1 + a)] |
Failure | Failure | Skip | Error |
| 8.19.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\genexpintE{p}@{t}\genexpintE{q}@{t}\diff{t} = \frac{L(p)+L(q)}{p+q-1}} | int(Ei(p, t)*Ei(q, t), t = 0..infinity)=(L*(p)+ L*(q))/(p + q - 1) |
Integrate[ExpIntegralE[p, t]*ExpIntegralE[q, t], {t, 0, Infinity}]=Divide[L*(p)+ L*(q),p + q - 1] |
Failure | Failure | Skip | Fail
Complex[-1.9874359859908697, -2.1876726427121085] <- {Rule[L, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.9874359859908697, -2.1876726427121085] <- {Rule[L, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.9874359859908697, 2.1876726427121085] <- {Rule[L, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.9874359859908697, 2.1876726427121085] <- {Rule[L, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[p, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 8.19.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L(p) = \int_{0}^{\infty}e^{-t}\genexpintE{p}@{t}\diff{t}} | L*(p)= int(exp(- t)*Ei(p, t), t = 0..infinity) |
L*(p)= Integrate[Exp[- t]*ExpIntegralE[p, t], {t, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 8.19.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-t}\genexpintE{p}@{t}\diff{t} = \frac{1}{2p}\hyperF@{1}{1}{1+p}{\tfrac{1}{2}}} | int(exp(- t)*Ei(p, t), t = 0..infinity)=(1)/(2*p)*hypergeom([1, 1], [1 + p], (1)/(2)) |
Integrate[Exp[- t]*ExpIntegralE[p, t], {t, 0, Infinity}]=Divide[1,2*p]*Hypergeometric2F1[1, 1, 1 + p, Divide[1,2]] |
Failure | Failure | Skip | Skip |
| 8.20.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genexpintE{p}@{z} = \frac{e^{-z}}{z}\left(\sum_{k=0}^{n-1}(-1)^{k}\frac{\Pochhammersym{p}{k}}{z^{k}}+(-1)^{n}\frac{\Pochhammersym{p}{n}e^{z}}{z^{n-1}}\genexpintE{n+p}@{z}\right)} | Ei(p, z)=(exp(- z))/(z)*(sum((- 1)^(k)*(pochhammer(p, k))/((z)^(k)), k = 0..n - 1)+(- 1)^(n)*(pochhammer(p, n)*exp(z))/((z)^(n - 1))*Ei(n + p, z)) |
ExpIntegralE[p, z]=Divide[Exp[- z],z]*(Sum[(- 1)^(k)*Divide[Pochhammer[p, k],(z)^(k)], {k, 0, n - 1}]+(- 1)^(n)*Divide[Pochhammer[p, n]*Exp[z],(z)^(n - 1)]*ExpIntegralE[n + p, z]) |
Failure | Successful | Skip | - |
| 8.20.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{k+1}(\lambda) = (1-2k\lambda)A_{k}(\lambda)+\lambda(\lambda+1)\deriv{A_{k}(\lambda)}{\lambda}} | A[k + 1]*(lambda)=(1 - 2*k*lambda)* A[k]*(lambda)+ lambda*(lambda + 1)* diff(A[k]*(lambda), lambda) |
Subscript[A, k + 1]*(\[Lambda])=(1 - 2*k*\[Lambda])* Subscript[A, k]*(\[Lambda])+ \[Lambda]*(\[Lambda]+ 1)* D[Subscript[A, k]*(\[Lambda]), \[Lambda]] |
Failure | Failure | Fail -28.28427122+24.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)+I*2^(1/2), k = 3}-24.28427122+20.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = 2^(1/2)-I*2^(1/2), k = 3}-28.28427122+16.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)-I*2^(1/2), k = 3}-32.28427122+20.28427123*I <- {lambda = 2^(1/2)+I*2^(1/2), A[k] = 2^(1/2)+I*2^(1/2), A[k+1] = -2^(1/2)+I*2^(1/2), k = 3}... skip entries to safe data |
Successful |
| 8.21.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{a-1}e^{+\iunit t}\diff{t} = e^{+\frac{1}{2}\pi\iunit a}\EulerGamma@{a}} | int((t)^(a - 1)* exp(+ I*t), t = 0..infinity)= exp(+(1)/(2)*Pi*I*a)*GAMMA(a) |
Integrate[(t)^(a - 1)* Exp[+ I*t], {t, 0, Infinity}]= Exp[+Divide[1,2]*Pi*I*a]*Gamma[a] |
Successful | Failure | - | Successful |
| 8.21.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{a-1}e^{-\iunit t}\diff{t} = e^{-\frac{1}{2}\pi\iunit a}\EulerGamma@{a}} | int((t)^(a - 1)* exp(- I*t), t = 0..infinity)= exp(-(1)/(2)*Pi*I*a)*GAMMA(a) |
Integrate[(t)^(a - 1)* Exp[- I*t], {t, 0, Infinity}]= Exp[-Divide[1,2]*Pi*I*a]*Gamma[a] |
Successful | Failure | - | Successful |
| 8.22.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\EulerGamma@{p}}{2\pi}z^{1-p}\genexpintE{p}@{z} = \frac{\EulerGamma@{p}}{2\pi}\incGamma@{1-p}{z}} | (GAMMA(p))/(2*Pi)*(z)^(1 - p)* Ei(p, z)=(GAMMA(p))/(2*Pi)*GAMMA(1 - p, z) |
Divide[Gamma[p],2*Pi]*(z)^(1 - p)* ExpIntegralE[p, z]=Divide[Gamma[p],2*Pi]*Gamma[1 - p, z] |
Successful | Successful | - | - |
| 8.22.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta_{x}(s) = \sum_{k=1}^{\infty}k^{-s}\normincGammaP@{s}{kx}} | zeta[x]*(s)= sum((k)^(- s)* (GAMMA(s)-GAMMA(s, k*x))/GAMMA(s), k = 1..infinity) |
Subscript[\[zeta], x]*(s)= Sum[(k)^(- s)* GammaRegularized[s, 0, k*x], {k, 1, Infinity}] |
Failure | Failure | Skip | Error |