19.12

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
19.12.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = \sum_{m=0}^{\infty}\frac{\Pochhammersym{\tfrac{1}{2}}{m}\Pochhammersym{\tfrac{1}{2}}{m}}{m!\;m!}{k^{\prime}}^{2m}\left(\ln@@{\left(\frac{1}{k^{\prime}}\right)}+d(m)\right)} \compellintKk@{k} = \sum_{m=0}^{\infty}\frac{\Pochhammersym{\tfrac{1}{2}}{m}\Pochhammersym{\tfrac{1}{2}}{m}}{m!\;m!}{k^{\prime}}^{2m}\left(\ln@@{\left(\frac{1}{k^{\prime}}\right)}+d(m)\right)	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < |k^{\prime}|, |k^{\prime}| < 1}	EllipticK(k) = sum((pochhammer((1)/(2), m)*pochhammer((1)/(2), m))/(factorial(m)*factorial(m))*(sqrt(1 - (k)^(2)))^(2*m)*(ln((1)/(sqrt(1 - (k)^(2))))+ d(m)), m = 0..infinity)	EllipticK[(k)^2] == Sum[Divide[Pochhammer[Divide[1,2], m]*Pochhammer[Divide[1,2], m],(m)!*(m)!]*(Sqrt[1 - (k)^(2)])^(2*m)*(Log[Divide[1,Sqrt[1 - (k)^(2)]]]+ d[m]), {m, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Error	Skip - No test values generated
19.12.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k} = 1+\frac{1}{2}\sum_{m=0}^{\infty}\frac{\Pochhammersym{\tfrac{1}{2}}{m}\Pochhammersym{\tfrac{3}{2}}{m}}{\Pochhammersym{2}{m}m!}{k^{\prime}}^{2m+2}\*\left(\ln@@{\left(\frac{1}{k^{\prime}}\right)}+d(m)-\frac{1}{(2m+1)(2m+2)}\right)} \compellintEk@{k} = 1+\frac{1}{2}\sum_{m=0}^{\infty}\frac{\Pochhammersym{\tfrac{1}{2}}{m}\Pochhammersym{\tfrac{3}{2}}{m}}{\Pochhammersym{2}{m}m!}{k^{\prime}}^{2m+2}\*\left(\ln@@{\left(\frac{1}{k^{\prime}}\right)}+d(m)-\frac{1}{(2m+1)(2m+2)}\right)	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |k^{\prime}| < 1}	EllipticE(k) = 1 +(1)/(2)*sum((pochhammer((1)/(2), m)*pochhammer((3)/(2), m))/(pochhammer(2, m)*factorial(m))*(sqrt(1 - (k)^(2)))^(2*m + 2)*(ln((1)/(sqrt(1 - (k)^(2))))+ d(m)-(1)/((2*m + 1)*(2*m + 2))), m = 0..infinity)	EllipticE[(k)^2] == 1 +Divide[1,2]*Sum[Divide[Pochhammer[Divide[1,2], m]*Pochhammer[Divide[3,2], m],Pochhammer[2, m]*(m)!]*(Sqrt[1 - (k)^(2)])^(2*m + 2)*(Log[Divide[1,Sqrt[1 - (k)^(2)]]]+ d[m]-Divide[1,(2*m + 1)*(2*m + 2)]), {m, 0, Infinity}, GenerateConditions->None]	Error	Failure	-	Failed [10 / 10] Result: Indeterminate Test Values: {Rule[d, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[k, 1]} Result: Indeterminate Test Values: {Rule[d, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]], Rule[k, 1]} ... skip entries to safe data
19.12#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d(m) = \digamma@{1+m}-\digamma@{\tfrac{1}{2}+m}} d(m) = \digamma@{1+m}-\digamma@{\tfrac{1}{2}+m}	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	d(m) = Psi(1 + m)- Psi((1)/(2)+ m)	d[m] == PolyGamma[1 + m]- PolyGamma[Divide[1,2]+ m]	Failure	Failure	Failed [30 / 30] Result: .4797310429+.5000000000*I Test Values: {d = 1/2*3^(1/2)+1/2*I, m = 1} Result: 1.512423114+1.*I Test Values: {d = 1/2*3^(1/2)+1/2*I, m = 2} ... skip entries to safe data	Failed [30 / 30] Result: Complex[0.04671834077232884, 0.24999999999999997] Test Values: {Rule[d, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[m, 1]} Result: Complex[0.6463977093312149, 0.49999999999999994] Test Values: {Rule[d, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[m, 2]} ... skip entries to safe data
19.12#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d(m+1) = d(m)-\frac{2}{(2m+1)(2m+2)}} d(m+1) = d(m)-\frac{2}{(2m+1)(2m+2)}	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	d(m + 1) = d(m)-(2)/((2*m + 1)*(2*m + 2))	d[m + 1] == d[m]-Divide[2,(2*m + 1)*(2*m + 2)]	Skipped - no semantic math	Skipped - no semantic math	-	-