Results of Gamma Function

DLMF	Formula	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
5.2.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{z} = \int_{0}^{\infty}e^{-t}t^{z-1}\diff{t}}	GAMMA(z) = int(exp(- t)*(t)^(z - 1), t = 0..infinity)	Gamma[z] == Integrate[Exp[- t]*(t)^(z - 1), {t, 0, Infinity}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 5]
5.2.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{z} = \EulerGamma'@{z}/\EulerGamma@{z}}	Psi(z) = diff( GAMMA(z), z$(1) )/ GAMMA(z)	PolyGamma[z] == D[Gamma[z], {z, 1}]/ Gamma[z]	Successful	Successful	-	Successful [Tested: 1]
5.2#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Pochhammersym{a}{0} = 1}	pochhammer(a, 0) = 1	Pochhammer[a, 0] == 1	Successful	Successful	-	Successful [Tested: 6]
5.2.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Pochhammersym{a}{n} = \EulerGamma@{a+n}/\EulerGamma@{a}}	pochhammer(a, n) = GAMMA(a + n)/ GAMMA(a)	Pochhammer[a, n] == Gamma[a + n]/ Gamma[a]	Successful	Successful	-	Successful [Tested: 3]
5.2.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Pochhammersym{-a}{n} = (-1)^{n}\Pochhammersym{a-n+1}{n}}	pochhammer(- a, n) = (- 1)^(n)* pochhammer(a - n + 1, n)	Pochhammer[- a, n] == (- 1)^(n)* Pochhammer[a - n + 1, n]	Failure	Failure	Successful [Tested: 18]	Successful [Tested: 18]
5.2#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Pochhammersym{a}{2n} = 2^{2n}\Pochhammersym{\frac{a}{2}}{n}\Pochhammersym{\frac{a+1}{2}}{n}}	pochhammer(a, 2*n) = (2)^(2*n)* pochhammer((a)/(2), n)*pochhammer((a + 1)/(2), n)	Pochhammer[a, 2*n] == (2)^(2*n)* Pochhammer[Divide[a,2], n]*Pochhammer[Divide[a + 1,2], n]	Successful	Successful	-	Successful [Tested: 18]
5.2#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Pochhammersym{a}{2n+1} = 2^{2n+1}\Pochhammersym{\frac{a}{2}}{n+1}\Pochhammersym{\frac{a+1}{2}}{n}}	pochhammer(a, 2*n + 1) = (2)^(2*n + 1)* pochhammer((a)/(2), n + 1)*pochhammer((a + 1)/(2), n)	Pochhammer[a, 2*n + 1] == (2)^(2*n + 1)* Pochhammer[Divide[a,2], n + 1]*Pochhammer[Divide[a + 1,2], n]	Successful	Successful	-	Successful [Tested: 18]
5.4#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{1} = 1}	GAMMA(1) = 1	Gamma[1] == 1	Successful	Successful	-	Successful [Tested: 1]
5.4#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n! = \EulerGamma@{n+1}}	factorial(n) = GAMMA(n + 1)	(n)! == Gamma[n + 1]	Successful	Successful	-	Successful [Tested: 3]
5.4.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\EulerGamma@{iy}| = \left(\frac{\pi}{y\sinh@{\pi y}}\right)^{1/2}}	abs(GAMMA(I*y)) = ((Pi)/(y*sinh(Pi*y)))^(1/ 2)	Abs[Gamma[I*y]] == (Divide[Pi,y*Sinh[Pi*y]])^(1/ 2)	Failure	Failure	Error	Skip - No test values generated
5.4.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\tfrac{1}{2}+\iunit y}\EulerGamma@{\tfrac{1}{2}-\iunit y} = \left|\EulerGamma@{\tfrac{1}{2}+\iunit y}\right|^{2}}	GAMMA((1)/(2)+ I*y)*GAMMA((1)/(2)- I*y) = (abs(GAMMA((1)/(2)+ I*y)))^(2)	Gamma[Divide[1,2]+ I*y]*Gamma[Divide[1,2]- I*y] == (Abs[Gamma[Divide[1,2]+ I*y]])^(2)	Failure	Failure	Successful [Tested: 6]	Successful [Tested: 6]
5.4.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left|\EulerGamma@{\tfrac{1}{2}+\iunit y}\right|^{2} = \frac{\pi}{\cosh@{\pi y}}}	(abs(GAMMA((1)/(2)+ I*y)))^(2) = (Pi)/(cosh(Pi*y))	(Abs[Gamma[Divide[1,2]+ I*y]])^(2) == Divide[Pi,Cosh[Pi*y]]	Failure	Failure	Successful [Tested: 6]	Successful [Tested: 6]
5.4.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\tfrac{1}{4}+\iunit y}\EulerGamma@{\tfrac{3}{4}-\iunit y} = \frac{\pi\sqrt{2}}{\cosh@{\pi y}+\iunit\sinh@{\pi y}}}	GAMMA((1)/(4)+ I*y)*GAMMA((3)/(4)- I*y) = (Pi*sqrt(2))/(cosh(Pi*y)+ I*sinh(Pi*y))	Gamma[Divide[1,4]+ I*y]*Gamma[Divide[3,4]- I*y] == Divide[Pi*Sqrt[2],Cosh[Pi*y]+ I*Sinh[Pi*y]]	Successful	Successful	-	Successful [Tested: 6]
5.4.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\tfrac{1}{2}} = \pi^{1/2}\\}	GAMMA((1)/(2)) = (Pi)^(1/ 2)	Gamma[Divide[1,2]] == (Pi)^(1/ 2)	Successful	Successful	-	Successful [Tested: 1]
5.4.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pi^{1/2}\\ = 1.77245\;38509\;05516\;02729\;\dots}	(Pi)^(1/ 2) = 1.77245385090551602729	(Pi)^(1/ 2) == 1.77245385090551602729	Successful	Successful	-	Successful [Tested: 1]
5.4.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\tfrac{1}{3}} = 2.67893\;85347\;07747\;63365\;\dots}	GAMMA((1)/(3)) = 2.67893853470774763365	Gamma[Divide[1,3]] == 2.67893853470774763365	Failure	Successful	Successful [Tested: 0]	Successful [Tested: 1]
5.4.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\tfrac{2}{3}} = 1.35411\;79394\;26400\;41694\;\dots}	GAMMA((2)/(3)) = 1.35411793942640041694	Gamma[Divide[2,3]] == 1.35411793942640041694	Successful	Successful	-	Successful [Tested: 1]
5.4.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\tfrac{1}{4}} = 3.62560\;99082\;21908\;31193\;\dots}	GAMMA((1)/(4)) = 3.62560990822190831193	Gamma[Divide[1,4]] == 3.62560990822190831193	Failure	Successful	Successful [Tested: 0]	Successful [Tested: 1]
5.4.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\tfrac{3}{4}} = 1.22541\;67024\;65177\;64512\;\dots}	GAMMA((3)/(4)) = 1.22541670246517764512	Gamma[Divide[3,4]] == 1.22541670246517764512	Successful	Successful	-	Successful [Tested: 1]
5.4.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma'@{1} = -\EulerConstant}	subs( temp=1, diff( GAMMA(temp), temp$(1) ) ) = - gamma	(D[Gamma[temp], {temp, 1}]/.temp-> 1) == - EulerGamma	Successful	Successful	-	Successful [Tested: 1]
5.4#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{1} = -\EulerConstant}	Psi(1) = - gamma	PolyGamma[1] == - EulerGamma	Successful	Successful	-	Successful [Tested: 1]
5.4#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma'@{1} = \tfrac{1}{6}\pi^{2}}	subs( temp=1, diff( Psi(temp), temp$(1) ) ) = (1)/(6)*(Pi)^(2)	(D[PolyGamma[temp], {temp, 1}]/.temp-> 1) == Divide[1,6]*(Pi)^(2)	Successful	Successful	-	Successful [Tested: 1]
5.4#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{\tfrac{1}{2}} = -\EulerConstant-2\ln@@{2}}	Psi((1)/(2)) = - gamma - 2*ln(2)	PolyGamma[Divide[1,2]] == - EulerGamma - 2*Log[2]	Successful	Successful	-	Successful [Tested: 1]
5.4#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma'@{\tfrac{1}{2}} = \tfrac{1}{2}\pi^{2}}	subs( temp=(1)/(2), diff( Psi(temp), temp$(1) ) ) = (1)/(2)*(Pi)^(2)	(D[PolyGamma[temp], {temp, 1}]/.temp-> Divide[1,2]) == Divide[1,2]*(Pi)^(2)	Successful	Successful	-	Successful [Tested: 1]
5.4.E14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{n+1} = \sum_{k=1}^{n}\frac{1}{k}-\EulerConstant}	Psi(n + 1) = sum((1)/(k), k = 1..n)- gamma	PolyGamma[n + 1] == Sum[Divide[1,k], {k, 1, n}, GenerateConditions->None]- EulerGamma	Successful	Successful	-	Successful [Tested: 3]
5.4.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \imagpart@@{\digamma@{iy}} = \frac{1}{2y}+\frac{\pi}{2}\coth@{\pi y}}	Im(Psi(I*y)) = (1)/(2*y)+(Pi)/(2)*coth(Pi*y)	Im[PolyGamma[I*y]] == Divide[1,2*y]+Divide[Pi,2]*Coth[Pi*y]	Failure	Failure	Successful [Tested: 6]	Successful [Tested: 6]
5.4.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \imagpart@@{\digamma@{\tfrac{1}{2}+iy}} = \frac{\pi}{2}\tanh@{\pi y}}	Im(Psi((1)/(2)+ I*y)) = (Pi)/(2)*tanh(Pi*y)	Im[PolyGamma[Divide[1,2]+ I*y]] == Divide[Pi,2]*Tanh[Pi*y]	Failure	Failure	Successful [Tested: 6]	Successful [Tested: 6]
5.4.E18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \imagpart@@{\digamma@{1+iy}} = -\frac{1}{2y}+\frac{\pi}{2}\coth@{\pi y}}	Im(Psi(1 + I*y)) = -(1)/(2*y)+(Pi)/(2)*coth(Pi*y)	Im[PolyGamma[1 + I*y]] == -Divide[1,2*y]+Divide[Pi,2]*Coth[Pi*y]	Failure	Failure	Successful [Tested: 6]	Successful [Tested: 6]
5.4.E19	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{\frac{p}{q}} = -\EulerConstant-\ln@@{q}-\frac{\pi}{2}\cot@{\frac{\pi p}{q}}+\frac{1}{2}\sum_{k=1}^{q-1}\cos@{\frac{2\pi kp}{q}}\ln@{2-2\cos@{\frac{2\pi k}{q}}}}	Psi((p)/(q)) = - gamma - ln(q)-(Pi)/(2)*cot((Pi*p)/(q))+(1)/(2)*sum(cos((2*Pi*k*p)/(q))*ln(2 - 2*cos((2*Pi*k)/(q))), k = 1..q - 1)	PolyGamma[Divide[p,q]] == - EulerGamma - Log[q]-Divide[Pi,2]*Cot[Divide[Pi*p,q]]+Divide[1,2]*Sum[Cos[Divide[2*Pi*k*p,q]]*Log[2 - 2*Cos[Divide[2*Pi*k,q]]], {k, 1, q - 1}, GenerateConditions->None]	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
5.5.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{z+1} = z\EulerGamma@{z}}	GAMMA(z + 1) = z*GAMMA(z)	Gamma[z + 1] == z*Gamma[z]	Successful	Successful	-	Successful [Tested: 5]
5.5.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{z+1} = \digamma@{z}+\frac{1}{z}}	Psi(z + 1) = Psi(z)+(1)/(z)	PolyGamma[z + 1] == PolyGamma[z]+Divide[1,z]	Successful	Successful	-	Successful [Tested: 7]
5.5.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{z}\EulerGamma@{1-z} = \pi/\sin@{\pi z}}	GAMMA(z)*GAMMA(1 - z) = Pi/ sin(Pi*z)	Gamma[z]*Gamma[1 - z] == Pi/ Sin[Pi*z]	Successful	Successful	-	Successful [Tested: 1]
5.5.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{z}-\digamma@{1-z} = -\pi/\tan@{\pi z}}	Psi(z)- Psi(1 - z) = - Pi/ tan(Pi*z)	PolyGamma[z]- PolyGamma[1 - z] == - Pi/ Tan[Pi*z]	Successful	Successful	-	Successful [Tested: 1]
5.5.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{2z} = \pi^{-1/2}2^{2z-1}\EulerGamma@{z}\EulerGamma@{z+\tfrac{1}{2}}}	GAMMA(2*z) = (Pi)^(- 1/ 2)* (2)^(2*z - 1)* GAMMA(z)*GAMMA(z +(1)/(2))	Gamma[2*z] == (Pi)^(- 1/ 2)* (2)^(2*z - 1)* Gamma[z]*Gamma[z +Divide[1,2]]	Successful	Successful	-	Successful [Tested: 5]
5.5.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{nz} = (2\pi)^{(1-n)/2}n^{nz-(1/2)}\prod_{k=0}^{n-1}\EulerGamma@{z+\frac{k}{n}}}	GAMMA(n*z) = (2*Pi)^((1 - n)/ 2)* (n)^(n*z -(1/ 2))* product(GAMMA(z +(k)/(n)), k = 0..n - 1)	Gamma[n*z] == (2*Pi)^((1 - n)/ 2)* (n)^(n*z -(1/ 2))* Product[Gamma[z +Divide[k,n]], {k, 0, n - 1}, GenerateConditions->None]	Failure	Successful	Successful [Tested: 15]	Successful [Tested: 15]
5.5.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \prod_{k=1}^{n-1}\EulerGamma@{\frac{k}{n}} = (2\pi)^{(n-1)/2}n^{-1/2}}	product(GAMMA((k)/(n)), k = 1..n - 1) = (2*Pi)^((n - 1)/ 2)* (n)^(- 1/ 2)	Product[Gamma[Divide[k,n]], {k, 1, n - 1}, GenerateConditions->None] == (2*Pi)^((n - 1)/ 2)* (n)^(- 1/ 2)	Failure	Failure	Successful [Tested: 3]	Failed [3 / 3] {Indeterminate <- {Rule[n, 1]} Indeterminate <- {Rule[n, 2]}
5.5.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{2z} = \tfrac{1}{2}\left(\digamma@{z}+\digamma@{z+\tfrac{1}{2}}\right)+\ln@@{2}}	Psi(2*z) = (1)/(2)*(Psi(z)+ Psi(z +(1)/(2)))+ ln(2)	PolyGamma[2*z] == Divide[1,2]*(PolyGamma[z]+ PolyGamma[z +Divide[1,2]])+ Log[2]	Successful	Successful	-	Successful [Tested: 7]
5.5.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{nz} = \frac{1}{n}\sum_{k=0}^{n-1}\digamma@{z+\frac{k}{n}}+\ln@@{n}}	Psi(n*z) = (1)/(n)*sum(Psi(z +(k)/(n)), k = 0..n - 1)+ ln(n)	PolyGamma[n*z] == Divide[1,n]*Sum[PolyGamma[z +Divide[k,n]], {k, 0, n - 1}, GenerateConditions->None]+ Log[n]	Failure	Successful	Successful [Tested: 21]	Successful [Tested: 21]
5.6.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 < (2\pi)^{-1/2}x^{(1/2)-x}e^{x}\EulerGamma@{x}}	1 < (2*Pi)^(- 1/ 2)* (x)^((1/ 2)- x)* exp(x)*GAMMA(x)	1 < (2*Pi)^(- 1/ 2)* (x)^((1/ 2)- x)* Exp[x]*Gamma[x]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
5.6.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (2\pi)^{-1/2}x^{(1/2)-x}e^{x}\EulerGamma@{x} < e^{1/(12x)}}	(2*Pi)^(- 1/ 2)* (x)^((1/ 2)- x)* exp(x)*GAMMA(x) < exp(1/(12*x))	(2*Pi)^(- 1/ 2)* (x)^((1/ 2)- x)* Exp[x]*Gamma[x] < Exp[1/(12*x)]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
5.6.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{x}}+\frac{1}{\EulerGamma@{1/x}} \leq 2}	(1)/(GAMMA(x))+(1)/(GAMMA(1/ x)) <= 2	Divide[1,Gamma[x]]+Divide[1,Gamma[1/ x]] <= 2	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
5.6.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{(\EulerGamma@{x})^{2}}+\frac{1}{(\EulerGamma@{1/x})^{2}} \leq 2}	(1)/((GAMMA(x))^(2))+(1)/((GAMMA(1/ x))^(2)) <= 2	Divide[1,(Gamma[x])^(2)]+Divide[1,(Gamma[1/ x])^(2)] <= 2	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
5.6.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{1-s} < \frac{\EulerGamma@{x+1}}{\EulerGamma@{x+s}}}	(x)^(1 - s) < (GAMMA(x + 1))/(GAMMA(x + s))	(x)^(1 - s) < Divide[Gamma[x + 1],Gamma[x + s]]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
5.6.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\EulerGamma@{x+1}}{\EulerGamma@{x+s}} < (x+1)^{1-s}}	(GAMMA(x + 1))/(GAMMA(x + s)) < (x + 1)^(1 - s)	Divide[Gamma[x + 1],Gamma[x + s]] < (x + 1)^(1 - s)	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
5.6.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \exp@{(1-s)\digamma@{x+s^{1/2}}} \leq \frac{\EulerGamma@{x+1}}{\EulerGamma@{x+s}}}	exp((1 - s)* Psi(x + (s)^(1/ 2))) <= (GAMMA(x + 1))/(GAMMA(x + s))	Exp[(1 - s)* PolyGamma[x + (s)^(1/ 2)]] <= Divide[Gamma[x + 1],Gamma[x + s]]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
5.6.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\EulerGamma@{x+1}}{\EulerGamma@{x+s}} \leq \exp@{(1-s)\digamma@{x+\tfrac{1}{2}(s+1)}}}	(GAMMA(x + 1))/(GAMMA(x + s)) <= exp((1 - s)* Psi(x +(1)/(2)*(s + 1)))	Divide[Gamma[x + 1],Gamma[x + s]] <= Exp[(1 - s)* PolyGamma[x +Divide[1,2]*(s + 1)]]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
5.6.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\EulerGamma@{x+\iunit y}| \leq |\EulerGamma@{x}|}	abs(GAMMA(x + I*y)) <= abs(GAMMA(x))	Abs[Gamma[x + I*y]] <= Abs[Gamma[x]]	Failure	Failure	Successful [Tested: 18]	Successful [Tested: 18]
5.6.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\EulerGamma@{x+\iunit y}| \geq (\sech@{\pi y})^{1/2}\EulerGamma@{x}}	abs(GAMMA(x + I*y)) >= (sech(Pi*y))^(1/ 2)* GAMMA(x)	Abs[Gamma[x + I*y]] >= (Sech[Pi*y])^(1/ 2)* Gamma[x]	Failure	Failure	Successful [Tested: 18]	Successful [Tested: 18]
5.6.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left|\frac{\EulerGamma@{z+a}}{\EulerGamma@{z+b}}\right| \leq \frac{1}{|z|^{b-a}}}	abs((GAMMA(z + a))/(GAMMA(z + b))) <= (1)/((abs(z))^(b - a))	Abs[Divide[Gamma[z + a],Gamma[z + b]]] <= Divide[1,(Abs[z])^(b - a)]	Failure	Failure	Failed [30 / 83] 30/83]: [[.5333333334 <= .1250000000 <- {a = -1.5, b = 1.5, z = 2} 2.000000000 <= .5000000000 <- {a = -1.5, b = -.5, z = 2} 1.333333334 <= .2500000000 <- {a = -1.5, b = .5, z = 2} .2954089752 <= .8838834764e-1 <- {a = -1.5, b = 2, z = 2} ... skip entries to safe data	Failed [35 / 95] {False <- {Rule[a, -1.5], Rule[b, 1.5], Rule[z, 2]} False <- {Rule[a, -1.5], Rule[b, -0.5], Rule[z, 2]}
5.6.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\EulerGamma@{z}| \leq (2\pi)^{1/2}|z|^{x-(1/2)}e^{-\pi|y|/2}\exp@{\tfrac{1}{6}|z|^{-1}}}	abs(GAMMA(x + y*I)) <= (2*Pi)^(1/ 2)*(abs(x + y*I))^(x -(1/ 2))* exp(- Pi*abs(y)/ 2)*exp((1)/(6)*(abs(x + y*I))^(- 1))	Abs[Gamma[x + y*I]] <= (2*Pi)^(1/ 2)*(Abs[x + y*I])^(x -(1/ 2))* Exp[- Pi*Abs[y]/ 2]*Exp[Divide[1,6]*(Abs[x + y*I])^(- 1)]	Failure	Failure	Successful [Tested: 18]	Successful [Tested: 18]
5.7.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{z}} = \sum_{k=1}^{\infty}c_{k}z^{k}}	(1)/(GAMMA(z)) = sum(c[k]*(z)^(k), k = 1..infinity)	Divide[1,Gamma[z]] == Sum[Subscript[c, k]*(z)^(k), {k, 1, Infinity}, GenerateConditions->None]	Failure	Failure	Failed [50 / 50] 50/50]: [[2.444337041-.9752791869*I <- {z = 1/2*3^(1/2)+1/2*I, c[k] = 1/2*3^(1/2)+1/2*I} 2.444337041+1.756771621*I <- {z = 1/2*3^(1/2)+1/2*I, c[k] = -1/2+1/2*I*3^(1/2)} -.287713767-.9752791869*I <- {z = 1/2*3^(1/2)+1/2*I, c[k] = 1/2-1/2*I*3^(1/2)} -.287713767+1.756771621*I <- {z = 1/2*3^(1/2)+1/2*I, c[k] = -1/2*3^(1/2)-1/2*I} ... skip entries to safe data	Failed [50 / 50] {Plus[Complex[1.0783116366515544, 0.3907462172966202], Times[-1.0, NSum[Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[1, k]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Plus[Complex[1.0783116366515544, 0.3907462172966202], Times[-1.0, NSum[Times[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, k], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
5.7.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{\EulerGamma@{1+z}} = -\ln@{1+z}+z(1-\EulerConstant)+\sum_{k=2}^{\infty}(-1)^{k}(\Riemannzeta@{k}-1)\frac{z^{k}}{k}}	ln(GAMMA(1 + z)) = - ln(1 + z)+ z*(1 - gamma)+ sum((- 1)^(k)*(Zeta(k)- 1)*((z)^(k))/(k), k = 2..infinity)	Log[Gamma[1 + z]] == - Log[1 + z]+ z*(1 - EulerGamma)+ Sum[(- 1)^(k)*(Zeta[k]- 1)*Divide[(z)^(k),k], {k, 2, Infinity}, GenerateConditions->None]	Failure	Successful	Successful [Tested: 6]	Successful [Tested: 6]
5.7.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{1+z} = -\EulerConstant+\sum_{k=2}^{\infty}(-1)^{k}\Riemannzeta@{k}z^{k-1}}	Psi(1 + z) = - gamma + sum((- 1)^(k)* Zeta(k)*(z)^(k - 1), k = 2..infinity)	PolyGamma[1 + z] == - EulerGamma + Sum[(- 1)^(k)* Zeta[k]*(z)^(k - 1), {k, 2, Infinity}, GenerateConditions->None]	Failure	Successful	Successful [Tested: 1]	Successful [Tested: 1]
5.7.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{1+z} = \frac{1}{2z}-\frac{\pi}{2}\cot@{\pi z}+\frac{1}{z^{2}-1}+1-\EulerConstant-\sum_{k=1}^{\infty}(\Riemannzeta@{2k+1}-1)z^{2k}}	Psi(1 + z) = (1)/(2*z)-(Pi)/(2)*cot(Pi*z)+(1)/((z)^(2)- 1)+ 1 - gamma - sum((Zeta(2*k + 1)- 1)* (z)^(2*k), k = 1..infinity)	PolyGamma[1 + z] == Divide[1,2*z]-Divide[Pi,2]*Cot[Pi*z]+Divide[1,(z)^(2)- 1]+ 1 - EulerGamma - Sum[(Zeta[2*k + 1]- 1)* (z)^(2*k), {k, 1, Infinity}, GenerateConditions->None]	Error	Successful	-	Successful [Tested: 6]
5.7.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{z} = -\EulerConstant-\frac{1}{z}+\sum_{k=1}^{\infty}\frac{z}{k(k+z)}}	Psi(z) = - gamma -(1)/(z)+ sum((z)/(k*(k + z)), k = 1..infinity)	PolyGamma[z] == - EulerGamma -Divide[1,z]+ Sum[Divide[z,k*(k + z)], {k, 1, Infinity}, GenerateConditions->None]	Failure	Successful	Successful [Tested: 7]	Successful [Tested: 7]
5.7.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\EulerConstant-\frac{1}{z}+\sum_{k=1}^{\infty}\frac{z}{k(k+z)} = -\EulerConstant+\sum_{k=0}^{\infty}\left(\frac{1}{k+1}-\frac{1}{k+z}\right)}	- gamma -(1)/(z)+ sum((z)/(k*(k + z)), k = 1..infinity) = - gamma + sum((1)/(k + 1)-(1)/(k + z), k = 0..infinity)	- EulerGamma -Divide[1,z]+ Sum[Divide[z,k*(k + z)], {k, 1, Infinity}, GenerateConditions->None] == - EulerGamma + Sum[Divide[1,k + 1]-Divide[1,k + z], {k, 0, Infinity}, GenerateConditions->None]	Failure	Successful	Successful [Tested: 7]	Successful [Tested: 7]
5.7.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{\frac{z+1}{2}}-\digamma@{\frac{z}{2}} = 2\sum_{k=0}^{\infty}\frac{(-1)^{k}}{k+z}}	Psi((z + 1)/(2))- Psi((z)/(2)) = 2*sum(((- 1)^(k))/(k + z), k = 0..infinity)	PolyGamma[Divide[z + 1,2]]- PolyGamma[Divide[z,2]] == 2*Sum[Divide[(- 1)^(k),k + z], {k, 0, Infinity}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 7]
5.7.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \imagpart@@{\digamma@{1+\iunit y}} = \sum_{k=1}^{\infty}\frac{y}{k^{2}+y^{2}}}	Im(Psi(1 + I*y)) = sum((y)/((k)^(2)+ (y)^(2)), k = 1..infinity)	Im[PolyGamma[1 + I*y]] == Sum[Divide[y,(k)^(2)+ (y)^(2)], {k, 1, Infinity}, GenerateConditions->None]	Failure	Failure	Successful [Tested: 6]	Successful [Tested: 6]
5.8.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{z}} = ze^{\EulerConstant z}\prod_{k=1}^{\infty}\left(1+\frac{z}{k}\right)e^{-z/k}}	(1)/(GAMMA(z)) = z*exp(gamma*z)*product((1 +(z)/(k))* exp(- z/ k), k = 1..infinity)	Divide[1,Gamma[z]] == z*Exp[EulerGamma*z]*Product[(1 +Divide[z,k])* Exp[- z/ k], {k, 1, Infinity}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 5]
5.8.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left|\frac{\EulerGamma@{x}}{\EulerGamma@{x+\iunit y}}\right|^{2} = \prod_{k=0}^{\infty}\left(1+\frac{y^{2}}{(x+k)^{2}}\right)}	(abs((GAMMA(x))/(GAMMA(x + I*y))))^(2) = product(1 +((y)^(2))/((x + k)^(2)), k = 0..infinity)	(Abs[Divide[Gamma[x],Gamma[x + I*y]]])^(2) == Product[1 +Divide[(y)^(2),(x + k)^(2)], {k, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Failed [18 / 18] 18/18]: [[-6.243891895+0.*I <- {x = 1.5, y = -1.5, x = 1} -6.243891895+0.*I <- {x = 1.5, y = 1.5, x = 1} -.210463144+0.*I <- {x = 1.5, y = -.5, x = 1} -.210463144+0.*I <- {x = 1.5, y = .5, x = 1} ... skip entries to safe data	Successful [Tested: 18]
5.9.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\mu}\EulerGamma@{\frac{\nu}{\mu}}\frac{1}{z^{\nu/\mu}} = \int_{0}^{\infty}\exp@{-zt^{\mu}}t^{\nu-1}\diff{t}}	(1)/(mu)*GAMMA((nu)/(mu))*(1)/((z)^(nu/ mu)) = int(exp(- z*(t)^(mu))*(t)^(nu - 1), t = 0..infinity)	Divide[1,\[Mu]]*Gamma[Divide[\[Nu],\[Mu]]]*Divide[1,(z)^(\[Nu]/ \[Mu])] == Integrate[Exp[- z*(t)^\[Mu]]*(t)^(\[Nu]- 1), {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Successful [Tested: 300]
5.9.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{z}} = \frac{1}{2\pi i}\int_{-\infty}^{(0+)}e^{t}t^{-z}\diff{t}}	(1)/(GAMMA(z)) = (1)/(2*Pi*I)*int(exp(t)*(t)^(- z), t = - infinity..(0 +))	Divide[1,Gamma[z]] == Divide[1,2*Pi*I]*Integrate[Exp[t]*(t)^(- z), {t, - Infinity, (0 +)}, GenerateConditions->None]	Error	Failure	-	Error
5.9.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c^{-z}\EulerGamma@{z} = \int_{-\infty}^{\infty}|t|^{2z-1}e^{-ct^{2}}\diff{t}}	(c)^(- z)* GAMMA(z) = int((abs(t))^(2*z - 1)* exp(- c*(t)^(2)), t = - infinity..infinity)	(c)^(- z)* Gamma[z] == Integrate[(Abs[t])^(2*z - 1)* Exp[- c*(t)^(2)], {t, - Infinity, Infinity}, GenerateConditions->None]	Missing Macro Error	Missing Macro Error	-	-
5.9.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{z} = \int_{1}^{\infty}t^{z-1}e^{-t}\diff{t}+\sum_{k=0}^{\infty}\frac{(-1)^{k}}{(z+k)k!}}	GAMMA(z) = int((t)^(z - 1)* exp(- t), t = 1..infinity)+ sum(((- 1)^(k))/((z + k)* factorial(k)), k = 0..infinity)	Gamma[z] == Integrate[(t)^(z - 1)* Exp[- t], {t, 1, Infinity}, GenerateConditions->None]+ Sum[Divide[(- 1)^(k),(z + k)* (k)!], {k, 0, Infinity}, GenerateConditions->None]	Failure	Successful	Failed [1 / 5] 1/5]: [[.9999999999-0.*I <- {z = 2, z = 1}	Successful [Tested: 1]
5.9.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{z} = \int_{0}^{\infty}t^{z-1}\left(e^{-t}-\sum_{k=0}^{n}\frac{(-1)^{k}t^{k}}{k!}\right)\diff{t}}	GAMMA(z) = int((t)^(z - 1)*(exp(- t)- sum(((- 1)^(k)* (t)^(k))/(factorial(k)), k = 0..n)), t = 0..infinity)	Gamma[z] == Integrate[(t)^(z - 1)*(Exp[- t]- Sum[Divide[(- 1)^(k)* (t)^(k),(k)!], {k, 0, n}, GenerateConditions->None]), {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Error	Skip - No test values generated
5.9.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{z}\cos@{\tfrac{1}{2}\pi z} = \int_{0}^{\infty}t^{z-1}\cos@@{t}\diff{t}}	GAMMA(z)*cos((1)/(2)*Pi*z) = int((t)^(z - 1)* cos(t), t = 0..infinity)	Gamma[z]*Cos[Divide[1,2]*Pi*z] == Integrate[(t)^(z - 1)* Cos[t], {t, 0, Infinity}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 3]
5.9.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{z}\sin@{\tfrac{1}{2}\pi z} = \int_{0}^{\infty}t^{z-1}\sin@@{t}\diff{t}}	GAMMA(z)*sin((1)/(2)*Pi*z) = int((t)^(z - 1)* sin(t), t = 0..infinity)	Gamma[z]*Sin[Divide[1,2]*Pi*z] == Integrate[(t)^(z - 1)* Sin[t], {t, 0, Infinity}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 3]
5.9.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{1+\frac{1}{n}}\cos@{\frac{\pi}{2n}} = \int_{0}^{\infty}\cos@{t^{n}}\diff{t}}	GAMMA(1 +(1)/(n))*cos((Pi)/(2*n)) = int(cos((t)^(n)), t = 0..infinity)	Gamma[1 +Divide[1,n]]*Cos[Divide[Pi,2*n]] == Integrate[Cos[(t)^(n)], {t, 0, Infinity}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 1]
5.9.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{1+\frac{1}{n}}\sin@{\frac{\pi}{2n}} = \int_{0}^{\infty}\sin@{t^{n}}\diff{t}}	GAMMA(1 +(1)/(n))*sin((Pi)/(2*n)) = int(sin((t)^(n)), t = 0..infinity)	Gamma[1 +Divide[1,n]]*Sin[Divide[Pi,2*n]] == Integrate[Sin[(t)^(n)], {t, 0, Infinity}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 1]
5.9.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Ln@@{\EulerGamma@{z}} = \left(z-\tfrac{1}{2}\right)\ln@@{z}-z+\tfrac{1}{2}\ln@{2\pi}+2\int_{0}^{\infty}\frac{\atan@{t/z}}{e^{2\pi t}-1}\diff{t}}	ln(GAMMA(z)) = (z -(1)/(2))* ln(z)- z +(1)/(2)*ln(2*Pi)+ 2*int((arctan(t/ z))/(exp(2*Pi*t)- 1), t = 0..infinity)	Log[Gamma[z]] == (z -Divide[1,2])* Log[z]- z +Divide[1,2]*Log[2*Pi]+ 2*Integrate[Divide[ArcTan[t/ z],Exp[2*Pi*t]- 1], {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Successful [Tested: 5]	Skipped - Because timed out
5.9.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Ln@@{\EulerGamma@{z+1}} = -\EulerConstant z-\frac{1}{2\pi i}\int_{-c-\infty i}^{-c+\infty i}\frac{\pi z^{-s}}{s\sin@{\pi s}}\Riemannzeta@{-s}\diff{s}}	ln(GAMMA(z + 1)) = - gamma*z -(1)/(2*Pi*I)*int((Pi*(z)^(- s))/(s*sin(Pi*s))*Zeta(- s), s = - c - infinity*I..- c + infinity*I)	Log[Gamma[z + 1]] == - EulerGamma*z -Divide[1,2*Pi*I]*Integrate[Divide[Pi*(z)^(- s),s*Sin[Pi*s]]*Zeta[- s], {s, - c - Infinity*I, - c + Infinity*I}, GenerateConditions->None]	Failure	Aborted	Failed [42 / 42] 42/42]: [[.3627983593+.4645558136*I <- {c = -1.5, z = 1/2*3^(1/2)+1/2*I} -.7321808519-.4375773776*I <- {c = -1.5, z = -1/2+1/2*I*3^(1/2)} -.1549651868-.6096201737*I <- {c = -1.5, z = 1/2-1/2*I*3^(1/2)} -.670593886e-1+1.175772123*I <- {c = -1.5, z = -1/2*3^(1/2)-1/2*I} ... skip entries to safe data	Skipped - Because timed out
5.9.E12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{z} = \int_{0}^{\infty}\left(\frac{e^{-t}}{t}-\frac{e^{-zt}}{1-e^{-t}}\right)\diff{t}}	Psi(z) = int((exp(- t))/(t)-(exp(- z*t))/(1 - exp(- t)), t = 0..infinity)	PolyGamma[z] == Integrate[Divide[Exp[- t],t]-Divide[Exp[- z*t],1 - Exp[- t]], {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Failed [2 / 7] 2/7]: [[Float(infinity)+Float(infinity)*I <- {z = -1/2+1/2*I*3^(1/2)} Float(infinity)+Float(infinity)*I <- {z = -1/2*3^(1/2)-1/2*I}	Successful [Tested: 1]
5.9.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{z} = \ln@@{z}+\int_{0}^{\infty}\left(\frac{1}{t}-\frac{1}{1-e^{-t}}\right)e^{-tz}\diff{t}}	Psi(z) = ln(z)+ int(((1)/(t)-(1)/(1 - exp(- t)))* exp(- t*z), t = 0..infinity)	PolyGamma[z] == Log[z]+ Integrate[(Divide[1,t]-Divide[1,1 - Exp[- t]])* Exp[- t*z], {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Failed [2 / 7] 2/7]: [[Float(infinity)+Float(infinity)*I <- {z = -1/2+1/2*I*3^(1/2)} Float(infinity)+Float(infinity)*I <- {z = -1/2*3^(1/2)-1/2*I}	Failed [1 / 1] {Indeterminate <- {Rule[z, 1]}
5.9.E14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{z} = \int_{0}^{\infty}\left(e^{-t}-\frac{1}{(1+t)^{z}}\right)\frac{\diff{t}}{t}}	Psi(z) = int((exp(- t)-(1)/((1 + t)^(z)))*(1)/(t), t = 0..infinity)	PolyGamma[z] == Integrate[(Exp[- t]-Divide[1,(1 + t)^(z)])*Divide[1,t], {t, 0, Infinity}, GenerateConditions->None]	Failure	Successful	Skipped - Because timed out	Successful [Tested: 7]
5.9.E15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{z} = \ln@@{z}-\frac{1}{2z}-2\int_{0}^{\infty}\frac{t\diff{t}}{(t^{2}+z^{2})(e^{2\pi t}-1)}}	Psi(z) = ln(z)-(1)/(2*z)- 2*int((t)/(((t)^(2)+ (z)^(2))*(exp(2*Pi*t)- 1)), t = 0..infinity)	PolyGamma[z] == Log[z]-Divide[1,2*z]- 2*Integrate[Divide[t,((t)^(2)+ (z)^(2))*(Exp[2*Pi*t]- 1)], {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Failed [2 / 7] 2/7]: [[.4e-10-.2711020420e-1*I <- {z = -1/2+1/2*I*3^(1/2)} -.2144560970-.1791125126*I <- {z = -1/2*3^(1/2)-1/2*I}	Successful [Tested: 1]
5.9.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{z}+\EulerConstant = \int_{0}^{\infty}\frac{e^{-t}-e^{-zt}}{1-e^{-t}}\diff{t}}	Psi(z)+ gamma = int((exp(- t)- exp(- z*t))/(1 - exp(- t)), t = 0..infinity)	PolyGamma[z]+ EulerGamma == Integrate[Divide[Exp[- t]- Exp[- z*t],1 - Exp[- t]], {t, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Failed [2 / 7] 2/7]: [[Float(infinity)+Float(infinity)*I <- {z = -1/2+1/2*I*3^(1/2)} Float(infinity)+Float(infinity)*I <- {z = -1/2*3^(1/2)-1/2*I}	Successful [Tested: 1]
5.9.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{e^{-t}-e^{-zt}}{1-e^{-t}}\diff{t} = \int_{0}^{1}\frac{1-t^{z-1}}{1-t}\diff{t}}	int((exp(- t)- exp(- z*t))/(1 - exp(- t)), t = 0..infinity) = int((1 - (t)^(z - 1))/(1 - t), t = 0..1)	Integrate[Divide[Exp[- t]- Exp[- z*t],1 - Exp[- t]], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[1 - (t)^(z - 1),1 - t], {t, 0, 1}, GenerateConditions->None]	Failure	Successful	Failed [2 / 7] 2/7]: [[Float(infinity)+Float(infinity)*I <- {z = -1/2+1/2*I*3^(1/2)} Float(infinity)+Float(infinity)*I <- {z = -1/2*3^(1/2)-1/2*I}	Successful [Tested: 7]
5.9.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{z+1} = -\EulerConstant+\frac{1}{2\pi i}\int_{-c-\infty i}^{-c+\infty i}\frac{\pi z^{-s-1}}{\sin@{\pi s}}\Riemannzeta@{-s}\diff{s}}	Psi(z + 1) = - gamma +(1)/(2*Pi*I)*int((Pi*(z)^(- s - 1))/(sin(Pi*s))*Zeta(- s), s = - c - infinity*I..- c + infinity*I)	PolyGamma[z + 1] == - EulerGamma +Divide[1,2*Pi*I]*Integrate[Divide[Pi*(z)^(- s - 1),Sin[Pi*s]]*Zeta[- s], {s, - c - Infinity*I, - c + Infinity*I}, GenerateConditions->None]	Failure	Failure	Failed [42 / 42] 42/42]: [[.9666504222+.3394950970*I <- {c = -1.5, z = 1/2*3^(1/2)+1/2*I} .3622891065+1.557241225*I <- {c = -1.5, z = -1/2+1/2*I*3^(1/2)} .8622891063-.6912158211*I <- {c = -1.5, z = 1/2-1/2*I*3^(1/2)} -.1138310784-2.481210069*I <- {c = -1.5, z = -1/2*3^(1/2)-1/2*I} ... skip entries to safe data	Skipped - Because timed out
5.9.E18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerConstant = -\int_{0}^{\infty}e^{-t}\ln@@{t}\diff{t}}	gamma = - int(exp(- t)*ln(t), t = 0..infinity)	EulerGamma == - Integrate[Exp[- t]*Log[t], {t, 0, Infinity}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 1]
5.9.E18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\int_{0}^{\infty}e^{-t}\ln@@{t}\diff{t} = \int_{0}^{\infty}\left(\frac{1}{1+t}-e^{-t}\right)\frac{\diff{t}}{t}}	- int(exp(- t)*ln(t), t = 0..infinity) = int(((1)/(1 + t)- exp(- t))*(1)/(t), t = 0..infinity)	- Integrate[Exp[- t]*Log[t], {t, 0, Infinity}, GenerateConditions->None] == Integrate[(Divide[1,1 + t]- Exp[- t])*Divide[1,t], {t, 0, Infinity}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 1]
5.9.E18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\left(\frac{1}{1+t}-e^{-t}\right)\frac{\diff{t}}{t} = \int_{0}^{1}(1-e^{-t})\frac{\diff{t}}{t}-\int_{1}^{\infty}e^{-t}\frac{\diff{t}}{t}}	int(((1)/(1 + t)- exp(- t))*(1)/(t), t = 0..infinity) = int((1 - exp(- t))*(1)/(t), t = 0..1)- int(exp(- t)*(1)/(t), t = 1..infinity)	Integrate[(Divide[1,1 + t]- Exp[- t])*Divide[1,t], {t, 0, Infinity}, GenerateConditions->None] == Integrate[(1 - Exp[- t])*Divide[1,t], {t, 0, 1}, GenerateConditions->None]- Integrate[Exp[- t]*Divide[1,t], {t, 1, Infinity}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 1]
5.9.E18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}(1-e^{-t})\frac{\diff{t}}{t}-\int_{1}^{\infty}e^{-t}\frac{\diff{t}}{t} = \int_{0}^{\infty}\left(\frac{e^{-t}}{1-e^{-t}}-\frac{e^{-t}}{t}\right)\diff{t}}	int((1 - exp(- t))*(1)/(t), t = 0..1)- int(exp(- t)*(1)/(t), t = 1..infinity) = int((exp(- t))/(1 - exp(- t))-(exp(- t))/(t), t = 0..infinity)	Integrate[(1 - Exp[- t])*Divide[1,t], {t, 0, 1}, GenerateConditions->None]- Integrate[Exp[- t]*Divide[1,t], {t, 1, Infinity}, GenerateConditions->None] == Integrate[Divide[Exp[- t],1 - Exp[- t]]-Divide[Exp[- t],t], {t, 0, Infinity}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 1]
5.9.E19	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma^{(n)}@{z} = \int_{0}^{\infty}(\ln@@{t})^{n}e^{-t}t^{z-1}\diff{t}}	diff( GAMMA(z), z$(n) ) = int((ln(t))^(n)* exp(- t)*(t)^(z - 1), t = 0..infinity)	D[Gamma[z], {z, n}] == Integrate[(Log[t])^(n)* Exp[- t]*(t)^(z - 1), {t, 0, Infinity}, GenerateConditions->None]	Successful	Aborted	-	Skipped - Because timed out
5.10#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{0} = \tfrac{1}{12}}	a[0] = (1)/(12)	Subscript[a, 0] == Divide[1,12]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.10#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{1} = \tfrac{1}{30}}	a[1] = (1)/(30)	Subscript[a, 1] == Divide[1,30]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.10#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{2} = \tfrac{53}{210}}	a[2] = (53)/(210)	Subscript[a, 2] == Divide[53,210]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.10#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{3} = \tfrac{195}{371}}	a[3] = (195)/(371)	Subscript[a, 3] == Divide[195,371]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.10#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{4} = \tfrac{22999}{22737}}	a[4] = (22999)/(22737)	Subscript[a, 4] == Divide[22999,22737]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.10#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{5} = \tfrac{299\;44523}{197\;33142}}	a[5] = (29944523)/(19733142)	Subscript[a, 5] == Divide[29944523,19733142]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.10#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{6} = \tfrac{10\;95352\;41009}{4\;82642\;75462}}	a[6] = (109535241009)/(48264275462)	Subscript[a, 6] == Divide[109535241009,48264275462]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.11#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{0} = 1}	g[0] = 1	Subscript[g, 0] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
5.11#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{1} = \tfrac{1}{12}}	g[1] = (1)/(12)	Subscript[g, 1] == Divide[1,12]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.11#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{2} = \tfrac{1}{288}}	g[2] = (1)/(288)	Subscript[g, 2] == Divide[1,288]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.11#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{3} = -\tfrac{139}{51840}}	g[3] = -(139)/(51840)	Subscript[g, 3] == -Divide[139,51840]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.11#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{4} = -\tfrac{571}{24\;88320}}	g[4] = -(571)/(2488320)	Subscript[g, 4] == -Divide[571,2488320]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.11#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{5} = \tfrac{1\;63879}{2090\;18880}}	g[5] = (163879)/(209018880)	Subscript[g, 5] == Divide[163879,209018880]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.11#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{6} = \tfrac{52\;46819}{7\;52467\;96800}}	g[6] = (5246819)/(75246796800)	Subscript[g, 6] == Divide[5246819,75246796800]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.11.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{k} = \sqrt{2}\Pochhammersym{\tfrac{1}{2}}{k}a_{2k}}	g[k] = sqrt(2)*pochhammer((1)/(2), k)*a[2*k]	Subscript[g, k] == Sqrt[2]*Pochhammer[Divide[1,2], k]*Subscript[a, 2*k]	Failure	Failure	Failed [300 / 300] 300/300]: [[.2536529683+.1464466095*I <- {a[2*k] = 1/2*3^(1/2)+1/2*I, g[k] = 1/2*3^(1/2)+1/2*I, k = 1} -.5253324962e-1-.303300858e-1*I <- {a[2*k] = 1/2*3^(1/2)+1/2*I, g[k] = 1/2*3^(1/2)+1/2*I, k = 2} -1.430371229-.8258252140*I <- {a[2*k] = 1/2*3^(1/2)+1/2*I, g[k] = 1/2*3^(1/2)+1/2*I, k = 3} -1.112372436+.5124720135*I <- {a[2*k] = 1/2*3^(1/2)+1/2*I, g[k] = -1/2+1/2*I*3^(1/2), k = 1} ... skip entries to safe data	Failed [300 / 300] {Complex[0.25365296808864424, 0.14644660940672627] <- {Rule[k, 1], Rule[Subscript[a, Times[2, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[-0.05253324975925311, -0.03033008588991054] <- {Rule[k, 2], Rule[Subscript[a, Times[2, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
5.11.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{z} = e^{-z}z^{z}\left(\frac{2\pi}{z}\right)^{1/2}\left(\sum_{k=0}^{K-1}\frac{g_{k}}{z^{k}}+R_{K}(z)\right)}	GAMMA(z) = exp(- z)*(z)^(z)*((2*Pi)/(z))^(1/ 2)*(sum((g[k])/((z)^(k)), k = 0..K - 1)+ R[K]*(z))	Gamma[z] == Exp[- z]*(z)^(z)*(Divide[2*Pi,z])^(1/ 2)*(Sum[Divide[Subscript[g, k],(z)^(k)], {k, 0, K - 1}, GenerateConditions->None]+ Subscript[R, K]*(z))	Failure	Failure	Failed [300 / 300] 300/300]: [[-1.892613380-.1706947928*I <- {K = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, R[K] = 1/2*3^(1/2)+1/2*I, g[k] = 1/2*3^(1/2)+1/2*I, K = 3} -.4529896033-2.955992714*I <- {K = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, R[K] = 1/2*3^(1/2)+1/2*I, g[k] = -1/2+1/2*I*3^(1/2), K = 3} .8926845412+1.268928985*I <- {K = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, R[K] = 1/2*3^(1/2)+1/2*I, g[k] = 1/2-1/2*I*3^(1/2), K = 3} 2.332308320-1.516368937*I <- {K = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, R[K] = 1/2*3^(1/2)+1/2*I, g[k] = -1/2*3^(1/2)-1/2*I, K = 3} ... skip entries to safe data	Failed [300 / 300] {Complex[-1.8926133813331316, -0.17069479199840365] <- {Rule[K, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[R, K], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[-0.7462398809799414, -0.22409723911500246] <- {Rule[K, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[R, K], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
5.11#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle G_{0}(a,b) = 1}	G[0]*(a , b) = 1	Subscript[G, 0]*(a , b) == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
5.11#Ex9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle G_{1}(a,b) = \tfrac{1}{2}(a-b)(a+b-1)}	G[1]*(a , b) = (1)/(2)*(a - b)*(a + b - 1)	Subscript[G, 1]*(a , b) == Divide[1,2]*(a - b)*(a + b - 1)	Skipped - no semantic math	Skipped - no semantic math	-	-
5.11#Ex10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle G_{2}(a,b) = \frac{1}{12}\binom{a-b}{2}(3(a+b-1)^{2}-(a-b+1))}	G[2]*(a , b) = (1)/(12)*binomial(a - b,2)*(3*(a + b - 1)^(2)-(a - b + 1))	Subscript[G, 2]*(a , b) == Divide[1,12]*Binomial[a - b,2]*(3*(a + b - 1)^(2)-(a - b + 1))	Failure	Failure	Error	Error
5.11#Ex11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle H_{0}(a,b) = 1}	H[0]*(a , b) = 1	Subscript[H, 0]*(a , b) == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
5.11#Ex12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle H_{1}(a,b) = -\frac{1}{12}\binom{a-b}{2}(a-b+1)}	H[1]*(a , b) = -(1)/(12)*binomial(a - b,2)*(a - b + 1)	Subscript[H, 1]*(a , b) == -Divide[1,12]*Binomial[a - b,2]*(a - b + 1)	Failure	Failure	Error	Error
5.11#Ex13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle H_{2}(a,b) = \frac{1}{240}\binom{a-b}{4}(2(a-b+1)+5(a-b+1)^{2})}	H[2]*(a , b) = (1)/(240)*binomial(a - b,4)*(2*(a - b + 1)+ 5*(a - b + 1)^(2))	Subscript[H, 2]*(a , b) == Divide[1,240]*Binomial[a - b,4]*(2*(a - b + 1)+ 5*(a - b + 1)^(2))	Failure	Failure	Error	Error
5.12.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerBeta@{a}{b} = \int_{0}^{1}t^{a-1}(1-t)^{b-1}\diff{t}}	Beta(a, b) = int((t)^(a - 1)*(1 - t)^(b - 1), t = 0..1)	Beta[a, b] == Integrate[(t)^(a - 1)*(1 - t)^(b - 1), {t, 0, 1}, GenerateConditions->None]	Failure	Successful	Error	Failed [11 / 36] {Indeterminate <- {Rule[a, -1.5], Rule[b, -2]} Indeterminate <- {Rule[a, 1.5], Rule[b, -2]}
5.12.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}t^{a-1}(1-t)^{b-1}\diff{t} = \frac{\EulerGamma@{a}\EulerGamma@{b}}{\EulerGamma@{a+b}}}	int((t)^(a - 1)*(1 - t)^(b - 1), t = 0..1) = (GAMMA(a)*GAMMA(b))/(GAMMA(a + b))	Integrate[(t)^(a - 1)*(1 - t)^(b - 1), {t, 0, 1}, GenerateConditions->None] == Divide[Gamma[a]*Gamma[b],Gamma[a + b]]	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 9]
5.12.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi/2}\sin^{2a-1}@@{\theta}\cos^{2b-1}@@{\theta}\diff{\theta} = \tfrac{1}{2}\EulerBeta@{a}{b}}	int((sin(theta))^(2*a - 1)* (cos(theta))^(2*b - 1), theta = 0..Pi/ 2) = (1)/(2)*Beta(a, b)	Integrate[(Sin[\[Theta]])^(2*a - 1)* (Cos[\[Theta]])^(2*b - 1), {\[Theta], 0, Pi/ 2}, GenerateConditions->None] == Divide[1,2]*Beta[a, b]	Failure	Successful	Error	Successful [Tested: 9]
5.12.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{t^{a-1}\diff{t}}{(1+t)^{a+b}} = \EulerBeta@{a}{b}}	int(((t)^(a - 1))/((1 + t)^(a + b)), t = 0..infinity) = Beta(a, b)	Integrate[Divide[(t)^(a - 1),(1 + t)^(a + b)], {t, 0, Infinity}, GenerateConditions->None] == Beta[a, b]	Failure	Successful	Error	Successful [Tested: 9]
5.12.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}\frac{t^{a-1}(1-t)^{b-1}}{(t+z)^{a+b}}\diff{t} = \EulerBeta@{a}{b}(1+z)^{-a}z^{-b}}	int(((t)^(a - 1)*(1 - t)^(b - 1))/((t + z)^(a + b)), t = 0..1) = Beta(a, b)*(1 + z)^(- a)* (z)^(- b)	Integrate[Divide[(t)^(a - 1)*(1 - t)^(b - 1),(t + z)^(a + b)], {t, 0, 1}, GenerateConditions->None] == Beta[a, b]*(1 + z)^(- a)* (z)^(- b)	Failure	Failure	Skipped - Because timed out	Failed [77 / 252] {Indeterminate <- {Rule[a, -1.5], Rule[b, -2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Indeterminate <- {Rule[a, -1.5], Rule[b, -2], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
5.12.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi/2}(\cos@@{t})^{a-1}\cos@{bt}\diff{t} = \frac{\pi}{2^{a}}\frac{1}{a\EulerBeta@{\frac{1}{2}(a+b+1)}{\frac{1}{2}(a-b+1)}}}	int((cos(t))^(a - 1)* cos(b*t), t = 0..Pi/ 2) = (Pi)/((2)^(a))*(1)/(a*Beta((1)/(2)*(a + b + 1), (1)/(2)*(a - b + 1)))	Integrate[(Cos[t])^(a - 1)* Cos[b*t], {t, 0, Pi/ 2}, GenerateConditions->None] == Divide[Pi,(2)^(a)]*Divide[1,a*Beta[Divide[1,2]*(a + b + 1), Divide[1,2]*(a - b + 1)]]	Failure	Aborted	Successful [Tested: 18]	Skipped - Because timed out
5.12.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi}(\sin@@{t})^{a-1}e^{ibt}\diff{t} = \frac{\pi}{2^{a-1}}\frac{e^{i\pi b/2}}{a\EulerBeta@{\frac{1}{2}(a+b+1)}{\frac{1}{2}(a-b+1)}}}	int((sin(t))^(a - 1)* exp(I*b*t), t = 0..Pi) = (Pi)/((2)^(a - 1))*(exp(I*Pi*b/ 2))/(a*Beta((1)/(2)*(a + b + 1), (1)/(2)*(a - b + 1)))	Integrate[(Sin[t])^(a - 1)* Exp[I*b*t], {t, 0, Pi}, GenerateConditions->None] == Divide[Pi,(2)^(a - 1)]*Divide[Exp[I*Pi*b/ 2],a*Beta[Divide[1,2]*(a + b + 1), Divide[1,2]*(a - b + 1)]]	Failure	Aborted	Successful [Tested: 18]	Failed [9 / 18] {DirectedInfinity[] <- {Rule[a, 1.5], Rule[b, -1.5]} DirectedInfinity[] <- {Rule[a, 1.5], Rule[b, 0.5]}
5.12.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{\cosh@{2bt}}{(\cosh@@{t})^{2a}}\diff{t} = 4^{a-1}\EulerBeta@{a+b}{a-b}}	int((cosh(2*b*t))/((cosh(t))^(2*a)), t = 0..infinity) = (4)^(a - 1)* Beta(a + b, a - b)	Integrate[Divide[Cosh[2*b*t],(Cosh[t])^(2*a)], {t, 0, Infinity}, GenerateConditions->None] == (4)^(a - 1)* Beta[a + b, a - b]	Failure	Failure	Successful [Tested: 6]	Successful [Tested: 6]
5.12.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int_{-\infty}^{\infty}\frac{\diff{t}}{(w+it)^{a}(z-it)^{b}} = \frac{(w+z)^{1-a-b}}{(a+b-1)\EulerBeta@{a}{b}}}	(1)/(2*Pi)*int((1)/((w + I*t)^(a)*(z - I*t)^(b)), t = - infinity..infinity) = ((w + z)^(1 - a - b))/((a + b - 1)* Beta(a, b))	Divide[1,2*Pi]*Integrate[Divide[1,(w + I*t)^(a)*(z - I*t)^(b)], {t, - Infinity, Infinity}, GenerateConditions->None] == Divide[(w + z)^(1 - a - b),(a + b - 1)* Beta[a, b]]	Skipped - Unable to analyze test case: Null	Failure	-	Successful [Tested: 250]
5.12.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi i}\int_{c-\infty i}^{c+\infty i}t^{-a}(1-t)^{-1-b}\diff{t} = \frac{1}{b\EulerBeta@{a}{b}}}	(1)/(2*Pi*I)*int((t)^(- a)*(1 - t)^(- 1 - b), t = c - infinity*I..c + infinity*I) = (1)/(b*Beta(a, b))	Divide[1,2*Pi*I]*Integrate[(t)^(- a)*(1 - t)^(- 1 - b), {t, c - Infinity*I, c + Infinity*I}, GenerateConditions->None] == Divide[1,b*Beta[a, b]]	Skipped - Unable to analyze test case: Null	Aborted	-	Skipped - Because timed out
5.12.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi i}\int_{0}^{(1+)}t^{a-1}(t-1)^{b-1}\diff{t} = \frac{\sin@{\pi b}}{\pi}\EulerBeta@{a}{b}}	(1)/(2*Pi*I)*int((t)^(a - 1)*(t - 1)^(b - 1), t = 0..(1 +)) = (sin(Pi*b))/(Pi)*Beta(a, b)	Divide[1,2*Pi*I]*Integrate[(t)^(a - 1)*(t - 1)^(b - 1), {t, 0, (1 +)}, GenerateConditions->None] == Divide[Sin[Pi*b],Pi]*Beta[a, b]	Skipped - Unable to analyze test case: Null	Failure	-	Error
5.12.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{e^{2\pi ia}-1}\int_{\infty}^{(0+)}t^{a-1}(1+t)^{-a-b}\diff{t} = \EulerBeta@{a}{b}}	(1)/(exp(2*Pi*I*a)- 1)*int((t)^(a - 1)*(1 + t)^(- a - b), t = infinity..(0 +)) = Beta(a, b)	Divide[1,Exp[2*Pi*I*a]- 1]*Integrate[(t)^(a - 1)*(1 + t)^(- a - b), {t, Infinity, (0 +)}, GenerateConditions->None] == Beta[a, b]	Error	Failure	-	Error
5.12.E12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{P}^{(1+,0+,1-,0-)}t^{a-1}(1-t)^{b-1}\diff{t} = -4e^{\pi i(a+b)}\sin@{\pi a}\sin@{\pi b}\EulerBeta@{a}{b}}	int((t)^(a - 1)*(1 - t)^(b - 1), t = P..(1 + , 0 + , 1 - , 0 -)) = - 4*exp(Pi*I*(a + b))*sin(Pi*a)*sin(Pi*b)*Beta(a, b)	Integrate[(t)^(a - 1)*(1 - t)^(b - 1), {t, P, (1 + , 0 + , 1 - , 0 -)}, GenerateConditions->None] == - 4*Exp[Pi*I*(a + b)]*Sin[Pi*a]*Sin[Pi*b]*Beta[a, b]	Error	Failure	-	Error
5.13.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{s+a}\EulerGamma@{b-s}z^{-s}\diff{s} = \frac{\EulerGamma@{a+b}z^{a}}{(1+z)^{a+b}}}	(1)/(2*Pi*I)*int(GAMMA(s + a)*GAMMA(b - s)*(z)^(- s), s = c - I*infinity..c + I*infinity) = (GAMMA(a + b)*(z)^(a))/((1 + z)^(a + b))	Divide[1,2*Pi*I]*Integrate[Gamma[s + a]*Gamma[b - s]*(z)^(- s), {s, c - I*Infinity, c + I*Infinity}, GenerateConditions->None] == Divide[Gamma[a + b]*(z)^(a),(1 + z)^(a + b)]	Skipped - Unable to analyze test case: Null	Aborted	-	Skipped - Because timed out
5.13.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int_{-\infty}^{\infty}|\EulerGamma@{a+it}|^{2}e^{(2b-\pi)t}\diff{t} = \frac{\EulerGamma@{2a}}{(2\sin@@{b})^{2a}}}	(1)/(2*Pi)*int((abs(GAMMA(a + I*t)))^(2)* exp((2*b - Pi)* t), t = - infinity..infinity) = (GAMMA(2*a))/((2*sin(b))^(2*a))	Divide[1,2*Pi]*Integrate[(Abs[Gamma[a + I*t]])^(2)* Exp[(2*b - Pi)* t], {t, - Infinity, Infinity}, GenerateConditions->None] == Divide[Gamma[2*a],(2*Sin[b])^(2*a)]	Skipped - Unable to analyze test case: Null	Aborted	-	Skipped - Because timed out
5.13.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int_{-\infty}^{\infty}\EulerGamma@{a+it}\EulerGamma@{b+it}\EulerGamma@{c-it}\EulerGamma@{d-it}\diff{t} = \frac{\EulerGamma@{a+c}\EulerGamma@{a+d}\EulerGamma@{b+c}\EulerGamma@{b+d}}{\EulerGamma@{a+b+c+d}}}	(1)/(2*Pi)*int(GAMMA(a + I*t)*GAMMA(b + I*t)*GAMMA(c - I*t)*GAMMA(d - I*t), t = - infinity..infinity) = (GAMMA(a + c)*GAMMA(a + d)*GAMMA(b + c)*GAMMA(b + d))/(GAMMA(a + b + c + d))	Divide[1,2*Pi]*Integrate[Gamma[a + I*t]*Gamma[b + I*t]*Gamma[c - I*t]*Gamma[d - I*t], {t, - Infinity, Infinity}, GenerateConditions->None] == Divide[Gamma[a + c]*Gamma[a + d]*Gamma[b + c]*Gamma[b + d],Gamma[a + b + c + d]]	Error	Aborted	-	Skipped - Because timed out
5.13.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}\frac{\diff{t}}{\EulerGamma@{a+t}\EulerGamma@{b+t}\EulerGamma@{c-t}\EulerGamma@{d-t}} = \frac{\EulerGamma@{a+b+c+d-3}}{\EulerGamma@{a+c-1}\EulerGamma@{a+d-1}\EulerGamma@{b+c-1}\EulerGamma@{b+d-1}}}	int((1)/(GAMMA(a + t)*GAMMA(b + t)*GAMMA(c - t)*GAMMA(d - t)), t = - infinity..infinity) = (GAMMA(a + b + c + d - 3))/(GAMMA(a + c - 1)*GAMMA(a + d - 1)*GAMMA(b + c - 1)*GAMMA(b + d - 1))	Integrate[Divide[1,Gamma[a + t]*Gamma[b + t]*Gamma[c - t]*Gamma[d - t]], {t, - Infinity, Infinity}, GenerateConditions->None] == Divide[Gamma[a + b + c + d - 3],Gamma[a + c - 1]*Gamma[a + d - 1]*Gamma[b + c - 1]*Gamma[b + d - 1]]	Failure	Aborted	Manual Skip!	Skipped - Because timed out
5.13.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{4\pi}\int_{-\infty}^{\infty}\frac{\prod_{k=1}^{4}\EulerGamma@{a_{k}+it}\EulerGamma@{a_{k}-it}}{\EulerGamma@{2it}\EulerGamma@{-2it}}\diff{t} = \frac{\prod_{1\leq j<k\leq 4}\EulerGamma@{a_{j}+a_{k}}}{\EulerGamma@{a_{1}+a_{2}+a_{3}+a_{4}}}}	(1)/(4*Pi)*int((product(GAMMA(a[k]+ I*t)*GAMMA(a[k]- I*t), k = 1..4))/(GAMMA(2*I*t)*GAMMA(- 2*I*t)), t = - infinity..infinity) = (product(product(GAMMA(a[j]+ a[k]), k = j + 1..4), j = 1..k - 1))/(GAMMA(a[1]+ a[2]+ a[3]+ a[4]))	Divide[1,4*Pi]*Integrate[Divide[Product[Gamma[Subscript[a, k]+ I*t]*Gamma[Subscript[a, k]- I*t], {k, 1, 4}, GenerateConditions->None],Gamma[2*I*t]*Gamma[- 2*I*t]], {t, - Infinity, Infinity}, GenerateConditions->None] == Divide[Product[Product[Gamma[Subscript[a, j]+ Subscript[a, k]], {k, j + 1, 4}, GenerateConditions->None], {j, 1, k - 1}, GenerateConditions->None],Gamma[Subscript[a, 1]+ Subscript[a, 2]+ Subscript[a, 3]+ Subscript[a, 4]]]	Error	Aborted	-	Skipped - Because timed out
5.15.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma'@{z} = \sum_{k=0}^{\infty}\frac{1}{(k+z)^{2}}}	diff( Psi(z), z$(1) ) = sum((1)/((k + z)^(2)), k = 0..infinity)	D[PolyGamma[z], {z, 1}] == Sum[Divide[1,(k + z)^(2)], {k, 0, Infinity}, GenerateConditions->None]	Failure	Successful	Successful [Tested: 0]	Successful [Tested: 1]
5.15.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \polygamma{n}@{1} = (-1)^{n+1}n!\Riemannzeta@{n+1}}	Psi(n, 1) = (- 1)^(n + 1)* factorial(n)*Zeta(n + 1)	PolyGamma[n, 1] == (- 1)^(n + 1)* (n)!*Zeta[n + 1]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
5.15.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \polygamma{n}@{\tfrac{1}{2}} = (-1)^{n+1}n!(2^{n+1}-1)\Riemannzeta@{n+1}}	Psi(n, (1)/(2)) = (- 1)^(n + 1)* factorial(n)*((2)^(n + 1)- 1)* Zeta(n + 1)	PolyGamma[n, Divide[1,2]] == (- 1)^(n + 1)* (n)!*((2)^(n + 1)- 1)* Zeta[n + 1]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
5.15.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma'@{n-\tfrac{1}{2}} = \tfrac{1}{2}\pi^{2}-4\sum_{k=1}^{n-1}\frac{1}{(2k-1)^{2}}}	subs( temp=n -(1)/(2), diff( Psi(temp), temp$(1) ) ) = (1)/(2)*(Pi)^(2)- 4*sum((1)/((2*k - 1)^(2)), k = 1..n - 1)	(D[PolyGamma[temp], {temp, 1}]/.temp-> n -Divide[1,2]) == Divide[1,2]*(Pi)^(2)- 4*Sum[Divide[1,(2*k - 1)^(2)], {k, 1, n - 1}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 3]
5.15.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma^{(n)}@{z+1} = \digamma^{(n)}@{z}+(-1)^{n}n!z^{-n-1}}	subs( temp=z + 1, diff( Psi(temp), temp$(n) ) ) = diff( Psi(z), z$(n) )+(- 1)^(n)* factorial(n)*(z)^(- n - 1)	(D[PolyGamma[temp], {temp, n}]/.temp-> z + 1) == D[PolyGamma[z], {z, n}]+(- 1)^(n)* (n)!*(z)^(- n - 1)	Failure	Failure	Successful [Tested: 21]	Successful [Tested: 21]
5.15.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma^{(n)}@{1-z}+(-1)^{n-1}\digamma^{(n)}@{z} = (-1)^{n}\pi\deriv[n]{}{z}\cot@{\pi z}}	subs( temp=1 - z, diff( Psi(temp), temp$(n) ) )+(- 1)^(n - 1)* diff( Psi(z), z$(n) ) = (- 1)^(n)* Pi*diff(cot(Pi*z), [z$(n)])	(D[PolyGamma[temp], {temp, n}]/.temp-> 1 - z)+(- 1)^(n - 1)* D[PolyGamma[z], {z, n}] == (- 1)^(n)* Pi*D[Cot[Pi*z], {z, n}]	Failure	Failure	Error	Failed [21 / 21] {Plus[Complex[-1.111486978443634, 1.4242909397222407], Times[Complex[-1.1253971041044755, 1.3474673991212198], Inactive[Sum][Times[Power[-0.5, K[1.0]], Power[Complex[2.0570132833277626, -0.06826349589921218], K[1.0]], Factorial[K[1.0]], StirlingS2[1.0, K[1.0]]] <- {K[1.0], 0.0, 1.0}]]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Plus[Complex[9.936030880873925, 6.770945349247037], Times[Complex[-8.466387364061939, -7.071078549251696], Inactive[Sum][Times[Power[-0.5, K[1.0]], Power[Complex[2.0570132833277626, -0.06826349589921218], K[1.0]], Factorial[K[1.0]], StirlingS2[2.0, K[1.0]]] <- {K[1.0], 0.0, 2.0}]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
5.15.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma^{(n)}@{mz} = \frac{1}{m^{n+1}}\sum_{k=0}^{m-1}\digamma^{(n)}@{z+\frac{k}{m}}}	diff( Psi(m*z), m*z$(n) ) = (1)/((m)^(n + 1))*sum(subs( temp=z +(k)/(m), diff( Psi(temp), temp$(n) ) ), k = 0..m - 1)	D[PolyGamma[m*z], {m*z, n}] == Divide[1,(m)^(n + 1)]*Sum[D[PolyGamma[temp], {temp, n}]/.temp-> z +Divide[k,m], {k, 0, m - 1}, GenerateConditions->None]	Error	Failure	-	Failed [63 / 63] {Plus[Complex[-1.1320242650810568, 1.0823171404691536], D[Complex[-0.4765906465900115, 0.839495097073875] <- {Complex[0.8660254037844387, 0.49999999999999994], 1.0}]], {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Plus[Complex[0.3478434500030721, -2.260508246850942], D[Complex[-0.4765906465900115, 0.839495097073875] <- {Complex[0.8660254037844387, 0.49999999999999994], 2.0}]], {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
5.16.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=1}^{\infty}(-1)^{k}\digamma'@{k} = -\frac{\pi^{2}}{8}}	sum((- 1)^(k)* diff( Psi(k), k$(1) ), k = 1..infinity) = -((Pi)^(2))/(8)	Sum[(- 1)^(k)* D[PolyGamma[k], {k, 1}], {k, 1, Infinity}, GenerateConditions->None] == -Divide[(Pi)^(2),8]	Failure	Successful	Successful [Tested: 0]	Successful [Tested: 1]
5.16.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=1}^{\infty}\frac{1}{k}\digamma'@{k+1} = \Riemannzeta@{3}}	sum((1)/(k)*subs( temp=k + 1, diff( Psi(temp), temp$(1) ) ), k = 1..infinity) = Zeta(3)	Sum[Divide[1,k]*(D[PolyGamma[temp], {temp, 1}]/.temp-> k + 1), {k, 1, Infinity}, GenerateConditions->None] == Zeta[3]	Failure	Successful	Successful [Tested: 0]	Successful [Tested: 1]
5.16.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemannzeta@{3} = -\frac{1}{2}\digamma''@{1}}	Zeta(3) = -(1)/(2)*subs( temp=1, diff( Psi(temp), temp$(2) ) )	Zeta[3] == -Divide[1,2]*(D[PolyGamma[temp], {temp, 2}]/.temp-> 1)	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 1]
5.17#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BarnesG@{z+1} = \EulerGamma@{z}\BarnesG@{z}}	Error	BarnesG[z + 1] == Gamma[z]*BarnesG[z]	Missing Macro Error	Failure	-	Successful [Tested: 5]
5.17#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BarnesG@{1} = 1}	Error	BarnesG[1] == 1	Missing Macro Error	Successful	-	Successful [Tested: 1]
5.17.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BarnesG@{z+1} = (2\pi)^{z/2}\exp@{-\tfrac{1}{2}z(z+1)-\tfrac{1}{2}\EulerConstant z^{2}}\*\prod_{k=1}^{\infty}\left(\left(1+\frac{z}{k}\right)^{k}\exp@{-z+\frac{z^{2}}{2k}}\right)}	Error	BarnesG[z + 1] == (2*Pi)^(z/ 2)* Exp[-Divide[1,2]*z*(z + 1)-Divide[1,2]*EulerGamma*(z)^(2)]* Product[(1 +Divide[z,k])^(k)* Exp[- z +Divide[(z)^(2),2*k]], {k, 1, Infinity}, GenerateConditions->None]	Missing Macro Error	Successful	-	Successful [Tested: 7]
5.17.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Ln@@{\BarnesG@{z+1}} = \tfrac{1}{2}z\ln@{2\pi}-\tfrac{1}{2}z(z+1)+z\Ln@@{\EulerGamma@{z+1}}-\int_{0}^{z}\Ln@@{\EulerGamma@{t+1}}\diff{t}}	Error	Log[BarnesG[z + 1]] == Divide[1,2]*z*Log[2*Pi]-Divide[1,2]*z*(z + 1)+ z*Log[Gamma[z + 1]]- Integrate[Log[Gamma[t + 1]], {t, 0, z}, GenerateConditions->None]	Missing Macro Error	Failure	-	Successful [Tested: 7]
5.17.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A = e^{C}}	A = exp(C)	A == Exp[C]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.17.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C = \lim_{n\to\infty}\left(\sum_{k=1}^{n}k\ln@@{k}-\left(\tfrac{1}{2}n^{2}+\tfrac{1}{2}n+\tfrac{1}{12}\right)\ln@@{n}+\tfrac{1}{4}n^{2}\right)}	C = limit(sum(k*ln(k), k = 1..n)-((1)/(2)*(n)^(2)+(1)/(2)*n +(1)/(12))* ln(n)+(1)/(4)*(n)^(2), n = infinity)	C == Limit[Sum[k*Log[k], {k, 1, n}, GenerateConditions->None]-(Divide[1,2]*(n)^(2)+Divide[1,2]*n +Divide[1,12])* Log[n]+Divide[1,4]*(n)^(2), n -> Infinity, GenerateConditions->None]	Failure	Failure	Failed [10 / 10] 10/10]: [[.6172709270+.5000000000*I <- {C = 1/2*3^(1/2)+1/2*I} -.7487544770+.8660254040*I <- {C = -1/2+1/2*I*3^(1/2)} .2512455230-.8660254040*I <- {C = 1/2-1/2*I*3^(1/2)} -1.114779881-.5000000000*I <- {C = -1/2*3^(1/2)-1/2*I} ... skip entries to safe data	Failed [10 / 10] {Complex[0.6172709267506544, 0.49999999999999994] <- {Rule[C, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[-0.7487544770337841, 0.8660254037844387] <- {Rule[C, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
5.17.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\left(\sum_{k=1}^{n}k\ln@@{k}-\left(\tfrac{1}{2}n^{2}+\tfrac{1}{2}n+\tfrac{1}{12}\right)\ln@@{n}+\tfrac{1}{4}n^{2}\right) = \frac{\EulerConstant+\ln@{2\pi}}{12}-\frac{\Riemannzeta'@{2}}{2\pi^{2}}}	limit(sum(k*ln(k), k = 1..n)-((1)/(2)*(n)^(2)+(1)/(2)*n +(1)/(12))* ln(n)+(1)/(4)*(n)^(2), n = infinity) = (gamma + ln(2*Pi))/(12)-(subs( temp=2, diff( Zeta(temp), temp$(1) ) ))/(2*(Pi)^(2))	Limit[Sum[k*Log[k], {k, 1, n}, GenerateConditions->None]-(Divide[1,2]*(n)^(2)+Divide[1,2]*n +Divide[1,12])* Log[n]+Divide[1,4]*(n)^(2), n -> Infinity, GenerateConditions->None] == Divide[EulerGamma + Log[2*Pi],12]-Divide[D[Zeta[temp], {temp, 1}]/.temp-> 2,2*(Pi)^(2)]	Failure	Successful	Successful [Tested: 0]	Successful [Tested: 1]
5.17.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\EulerConstant+\ln@{2\pi}}{12}-\frac{\Riemannzeta'@{2}}{2\pi^{2}} = \frac{1}{12}-\Riemannzeta'@{-1}}	(gamma + ln(2*Pi))/(12)-(subs( temp=2, diff( Zeta(temp), temp$(1) ) ))/(2*(Pi)^(2)) = (1)/(12)- subs( temp=- 1, diff( Zeta(temp), temp$(1) ) )	Divide[EulerGamma + Log[2*Pi],12]-Divide[D[Zeta[temp], {temp, 1}]/.temp-> 2,2*(Pi)^(2)] == Divide[1,12]- (D[Zeta[temp], {temp, 1}]/.temp-> - 1)	Failure	Successful	Successful [Tested: 0]	Successful [Tested: 1]
5.18.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{a}{q}{n} = \prod_{k=0}^{n-1}(1-aq^{k})}	QPochhammer(a, q, n) = product(1 - a*(q)^(k), k = 0..n - 1)	QPochhammer[a, q, n] == Product[1 - a*(q)^(k), {k, 0, n - 1}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 60]
5.18.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{a}{q}{\infty} = \prod_{k=0}^{\infty}(1-aq^{k})}	QPochhammer(a, q, infinity) = product(1 - a*(q)^(k), k = 0..infinity)	QPochhammer[a, q, Infinity] == Product[1 - a*(q)^(k), {k, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Error	Failed [48 / 60] {Plus[Times[-1.0, QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994]]], QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]] <- {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Indeterminate <- {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
5.18.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qGamma{q}@{z} = \qPochhammer{q}{q}{\infty}(1-q)^{1-z}/\qPochhammer{q^{z}}{q}{\infty}}	QGAMMA(q, z) = QPochhammer(q, q, infinity)*(1 - q)^(1 - z)/ QPochhammer((q)^(z), q, infinity)	QGamma[z,q] == QPochhammer[q, q, Infinity]*(1 - q)^(1 - z)/ QPochhammer[(q)^(z), q, Infinity]	Error	Failure	-	Failed [56 / 70] {Plus[QGamma[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[-0.4701974928403924, -0.07292434984262404], Power[QPochhammer[Complex[0.6918839380246471, 0.3371668184918191], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]] <- {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Plus[QGamma[Complex[-0.4999999999999998, 0.8660254037844387], Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[-0.021172596861766507, 0.11798586945608598], Power[QPochhammer[Complex[0.6137803977754971, -0.16446196191399762], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387,
5.18.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qGamma{q}@{1} = \qGamma{q}@{2}}	QGAMMA(q, 1) = QGAMMA(q, 2)	QGamma[1,q] == QGamma[2,q]	Error	Successful	-	Successful [Tested: 10]
5.18.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qGamma{q}@{2} = 1}	QGAMMA(q, 2) = 1	QGamma[2,q] == 1	Error	Successful	-	Successful [Tested: 10]
5.18.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qfactorial{n}{q} = \qGamma{q}@{n+1}}	QFactorial(n, q) = QGAMMA(q, n + 1)	QFactorial[n,q] == QGamma[n + 1,q]	Error	Successful	-	Successful [Tested: 30]
5.18.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qGamma{q}@{z+1} = \frac{1-q^{z}}{1-q}\qGamma{q}@{z}}	QGAMMA(q, z + 1) = (1 - (q)^(z))/(1 - q)*QGAMMA(q, z)	QGamma[z + 1,q] == Divide[1 - (q)^(z),1 - q]*QGamma[z,q]	Error	Failure	-	Failed [17 / 70] {Indeterminate <- {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Indeterminate <- {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
5.18.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qGamma{q}@{x} < \qGamma{r}@{x}}	QGAMMA(q, x) < QGAMMA(r, x)	QGamma[x,q] < QGamma[x,r]	Failure	Failure	Error	Failed [174 / 180] {Less[QGamma[1.5, Complex[0.8660254037844387, 0.49999999999999994]], Complex[0.4591522571856908, -0.3749002120921232]] <- {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[x, 1.5]} Less[QGamma[0.5, Complex[0.8660254037844387, 0.49999999999999994]], Complex[4.854857756142472*^-6, 0.9372445842681697]] <- {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[x, 0.5]}
5.18.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qGamma{q}@{x} > \qGamma{r}@{x}}	QGAMMA(q, x) > QGAMMA(r, x)	QGamma[x,q] > QGamma[x,r]	Failure	Failure	Error	Failed [174 / 180] {Greater[QGamma[1.5, Complex[0.8660254037844387, 0.49999999999999994]], Complex[0.4591522571856908, -0.3749002120921232]] <- {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[x, 1.5]} Greater[QGamma[0.5, Complex[0.8660254037844387, 0.49999999999999994]], Complex[4.854857756142472*^-6, 0.9372445842681697]] <- {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[x, 0.5]}
5.18.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{q\to 1-}\qGamma{q}@{z} = \EulerGamma@{z}}	limit(QGAMMA(q, z), q = 1, left) = GAMMA(z)	Limit[QGamma[z,q], q -> 1, Direction -> "FromBelow", GenerateConditions->None] == Gamma[z]	Failure	Aborted	Error	Skipped - Because timed out
5.19#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S = \sum_{k=0}^{\infty}a_{k}}	S = sum(a[k], k = 0..infinity)	S == Sum[Subscript[a, k], {k, 0, Infinity}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.19#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{k} = \frac{k}{(3k+2)(2k+1)(k+1)}}	a[k] = (k)/((3*k + 2)*(2*k + 1)*(k + 1))	Subscript[a, k] == Divide[k,(3*k + 2)*(2*k + 1)*(k + 1)]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.19.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{k} = \frac{2}{k+\frac{2}{3}}-\frac{1}{k+\frac{1}{2}}-\frac{1}{k+1}}	a[k] = (2)/(k +(2)/(3))-(1)/(k +(1)/(2))-(1)/(k + 1)	Subscript[a, k] == Divide[2,k +Divide[2,3]]-Divide[1,k +Divide[1,2]]-Divide[1,k + 1]	Skipped - no semantic math	Skipped - no semantic math	-	-
5.19.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S = \digamma@{\tfrac{1}{2}}-2\digamma@{\tfrac{2}{3}}-\EulerConstant}	S = Psi((1)/(2))- 2*Psi((2)/(3))- gamma	S == PolyGamma[Divide[1,2]]- 2*PolyGamma[Divide[2,3]]- EulerGamma	Failure	Failure	Failed [10 / 10] 10/10]: [[.7702822630+.5000000000*I <- {S = 1/2*3^(1/2)+1/2*I} -.5957431410+.8660254040*I <- {S = -1/2+1/2*I*3^(1/2)} .4042568590-.8660254040*I <- {S = 1/2-1/2*I*3^(1/2)} -.9617685450-.5000000000*I <- {S = -1/2*3^(1/2)-1/2*I} ... skip entries to safe data	Failed [10 / 10] {Complex[0.7702822631342183, 0.49999999999999994] <- {Rule[S, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[-0.5957431406502202, 0.8660254037844387] <- {Rule[S, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
5.19.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{\tfrac{1}{2}}-2\digamma@{\tfrac{2}{3}}-\EulerConstant = 3\ln@@{3}-2\ln@@{2}-\tfrac{1}{3}\pi\sqrt{3}}	Psi((1)/(2))- 2*Psi((2)/(3))- gamma = 3*ln(3)- 2*ln(2)-(1)/(3)*Pi*sqrt(3)	PolyGamma[Divide[1,2]]- 2*PolyGamma[Divide[2,3]]- EulerGamma == 3*Log[3]- 2*Log[2]-Divide[1,3]*Pi*Sqrt[3]	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 1]
5.19#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V = \frac{\pi^{\frac{1}{2}n}r^{n}}{\EulerGamma@{\frac{1}{2}n+1}}}	V = ((Pi)^((1)/(2)*n)* (r)^(n))/(GAMMA((1)/(2)*n + 1))	V == Divide[(Pi)^(Divide[1,2]*n)* (r)^(n),Gamma[Divide[1,2]*n + 1]]	Failure	Failure	Failed [180 / 180] 180/180]: [[3.866025403+.5000000000*I <- {V = 1/2*3^(1/2)+1/2*I, r = -1.5, n = 1} -6.202558068+.5000000000*I <- {V = 1/2*3^(1/2)+1/2*I, r = -1.5, n = 2} 15.00319234+.5000000000*I <- {V = 1/2*3^(1/2)+1/2*I, r = -1.5, n = 3} -2.133974595+.5000000000*I <- {V = 1/2*3^(1/2)+1/2*I, r = 1.5, n = 1} ... skip entries to safe data	Failed [180 / 180] {Complex[3.866025403784439, 0.49999999999999994] <- {Rule[n, 1], Rule[r, -1.5], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[-6.202558066792596, 0.49999999999999994] <- {Rule[n, 2], Rule[r, -1.5], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
5.19#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S = \frac{2\pi^{\frac{1}{2}n}r^{n-1}}{\EulerGamma@{\frac{1}{2}n}}}	S = (2*(Pi)^((1)/(2)*n)* (r)^(n - 1))/(GAMMA((1)/(2)*n))	S == Divide[2*(Pi)^(Divide[1,2]*n)* (r)^(n - 1),Gamma[Divide[1,2]*n]]	Failure	Failure	Failed [174 / 180] 174/180]: [[-1.133974596+.5000000000*I <- {S = 1/2*3^(1/2)+1/2*I, r = -1.5, n = 1} 10.29080337+.5000000000*I <- {S = 1/2*3^(1/2)+1/2*I, r = -1.5, n = 2} -27.40830850+.5000000000*I <- {S = 1/2*3^(1/2)+1/2*I, r = -1.5, n = 3} -1.133974596+.5000000000*I <- {S = 1/2*3^(1/2)+1/2*I, r = 1.5, n = 1} ... skip entries to safe data	Failed [174 / 180] {Complex[-1.1339745962155612, 0.49999999999999994] <- {Rule[n, 1], Rule[r, -1.5], Rule[S, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[10.290803364553819, 0.49999999999999994] <- {Rule[n, 2], Rule[r, -1.5], Rule[S, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
5.19#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2\pi^{\frac{1}{2}n}r^{n-1}}{\EulerGamma@{\frac{1}{2}n}} = \frac{n}{r}V}	(2*(Pi)^((1)/(2)*n)* (r)^(n - 1))/(GAMMA((1)/(2)*n)) = (n)/(r)*V	Divide[2*(Pi)^(Divide[1,2]*n)* (r)^(n - 1),Gamma[Divide[1,2]*n]] == Divide[n,r]*V	Failure	Failure	Failed [180 / 180] 180/180]: [[2.577350269+.3333333334*I <- {V = 1/2*3^(1/2)+1/2*I, r = -1.5, n = 1} -8.270077424+.6666666665*I <- {V = 1/2*3^(1/2)+1/2*I, r = -1.5, n = 2} 30.00638471+1.000000000*I <- {V = 1/2*3^(1/2)+1/2*I, r = -1.5, n = 3} 1.422649731-.3333333334*I <- {V = 1/2*3^(1/2)+1/2*I, r = 1.5, n = 1} ... skip entries to safe data	Failed [180 / 180] {Complex[2.5773502691896253, 0.33333333333333326] <- {Rule[n, 1], Rule[r, -1.5], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[-8.270077422390127, 0.6666666666666665] <- {Rule[n, 2], Rule[r, -1.5], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
5.20.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle W = \frac{1}{2}\sum_{\ell=1}^{n}x_{\ell}^{2}-\sum_{1\leq\ell<j\leq n}\ln@@{|x_{\ell}-x_{j}|}}	W = sum(x(x[ell])^(2), ell = 1..n)- sum(sum(ln(abs(x[ell]- x[j])), j = ell + 1..n), ell = 1..j - 1)	W == Sum[x(Subscript[x, \[ScriptL]])^(2), {\[ScriptL], 1, n}, GenerateConditions->None]- Sum[Sum[Log[Abs[Subscript[x, \[ScriptL]]- Subscript[x, j]]], {j, [ScriptL] + 1, n}, GenerateConditions->None], {\[ScriptL], 1, j - 1}, GenerateConditions->None]	Failure	Failure	Error	Error
5.20.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle W = -\sum_{1\leq\ell<j\leq n}\ln@@{|e^{i\theta_{\ell}}-e^{i\theta_{j}}|}}	W = - sum(sum(ln(abs(exp(I*theta[ell])- exp(I*theta[j]))), j = ell + 1..n), ell = 1..j - 1)	W == - Sum[Sum[Log[Abs[Exp[I*Subscript[\[Theta], \[ScriptL]]]- Exp[I*Subscript[\[Theta], j]]]], {j, [ScriptL] + 1, n}, GenerateConditions->None], {\[ScriptL], 1, j - 1}, GenerateConditions->None]	Failure	Failure	Error	Error