Generalized Hypergeometric Functions & Meijer G -Function - 16.12 Products

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
16.12.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genhyperF{0}{1}@{-}{a}{z}\genhyperF{0}{1}@{-}{b}{z} = \genhyperF{2}{3}@@{\frac{1}{2}(a+b),\frac{1}{2}(a+b-1)}{a,b,a+b-1}{4z}} \genhyperF{0}{1}@{-}{a}{z}\genhyperF{0}{1}@{-}{b}{z} = \genhyperF{2}{3}@@{\frac{1}{2}(a+b),\frac{1}{2}(a+b-1)}{a,b,a+b-1}{4z}	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	hypergeom([-], [a], z)*hypergeom([-], [b], z) = hypergeom([(1)/(2)*(a + b),(1)/(2)*(a + b - 1)], [a , b , a + b - 1], 4*z)	HypergeometricPFQ[{-}, {a}, z]*HypergeometricPFQ[{-}, {b}, z] == HypergeometricPFQ[{Divide[1,2]*(a + b),Divide[1,2]*(a + b - 1)}, {a , b , a + b - 1}, 4*z]	Error	Failure	-	Error
16.12.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\genhyperF{2}{1}@@{a,b}{a+b+\frac{1}{2}}{z}\right)^{2} = \genhyperF{3}{2}@@{2a,2b,a+b}{a+b+\frac{1}{2},2a+2b}{z}} \left(\genhyperF{2}{1}@@{a,b}{a+b+\frac{1}{2}}{z}\right)^{2} = \genhyperF{3}{2}@@{2a,2b,a+b}{a+b+\frac{1}{2},2a+2b}{z}	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	(hypergeom([a , b], [a + b +(1)/(2)], z))^(2) = hypergeom([2*a , 2*b , a + b], [a + b +(1)/(2), 2*a + 2*b], z)	(HypergeometricPFQ[{a , b}, {a + b +Divide[1,2]}, z])^(2) == HypergeometricPFQ[{2*a , 2*b , a + b}, {a + b +Divide[1,2], 2*a + 2*b}, z]	Failure	Failure	Manual Skip!	Failed [108 / 252] Result: Complex[4.205771365940054, 0.2846096908265261] Test Values: {Rule[a, -1.5], Rule[b, 1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-23.50000000000001, -28.578838324886455] Test Values: {Rule[a, -1.5], Rule[b, 1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
16.12.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\genhyperF{2}{1}@@{a,b}{c}{z}\right)^{2} = \sum_{k=0}^{\infty}\frac{\Pochhammersym{2a}{k}\Pochhammersym{2b}{k}\Pochhammersym{c-\frac{1}{2}}{k}}{\Pochhammersym{c}{k}\Pochhammersym{2c-1}{k}k!}\genhyperF{4}{3}@@{-\frac{1}{2}k,\frac{1}{2}(1-k),a+b-c+\frac{1}{2},\frac{1}{2}}{a+\frac{1}{2},b+\frac{1}{2},\frac{3}{2}-k-c}{1}z^{k}} \left(\genhyperF{2}{1}@@{a,b}{c}{z}\right)^{2} = \sum_{k=0}^{\infty}\frac{\Pochhammersym{2a}{k}\Pochhammersym{2b}{k}\Pochhammersym{c-\frac{1}{2}}{k}}{\Pochhammersym{c}{k}\Pochhammersym{2c-1}{k}k!}\genhyperF{4}{3}@@{-\frac{1}{2}k,\frac{1}{2}(1-k),a+b-c+\frac{1}{2},\frac{1}{2}}{a+\frac{1}{2},b+\frac{1}{2},\frac{3}{2}-k-c}{1}z^{k}	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |z| < 1}	(hypergeom([a , b], [c], z))^(2) = sum((pochhammer(2*a, k)*pochhammer(2*b, k)*pochhammer(c -(1)/(2), k))/(pochhammer(c, k)*pochhammer(2*c - 1, k)*factorial(k))*hypergeom([-(1)/(2)*k ,(1)/(2)*(1 - k), a + b - c +(1)/(2),(1)/(2)], [a +(1)/(2), b +(1)/(2),(3)/(2)- k - c], 1)*(z)^(k), k = 0..infinity)	(HypergeometricPFQ[{a , b}, {c}, z])^(2) == Sum[Divide[Pochhammer[2*a, k]*Pochhammer[2*b, k]*Pochhammer[c -Divide[1,2], k],Pochhammer[c, k]*Pochhammer[2*c - 1, k]*(k)!]*HypergeometricPFQ[{-Divide[1,2]*k ,Divide[1,2]*(1 - k), a + b - c +Divide[1,2],Divide[1,2]}, {a +Divide[1,2], b +Divide[1,2],Divide[3,2]- k - c}, 1]*(z)^(k), {k, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Failed [159 / 216] Result: -.1250000000 Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2} Result: 5.872053804 Test Values: {a = -3/2, b = -3/2, c = -1/2, z = 1/2} ... skip entries to safe data	Skipped - Because timed out