Generalized Hypergeometric Functions & Meijer G -Function - 16.6 Transformations of Variable

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
16.6.E1	${\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a,b,c\atop a-b+1,a-c+1};z\right)=(1-z)^{-a}{{}_{3}F_{2}}\left({a-b-c+1,\frac{1}{2}a,\frac{1}{2}(a+1)\atop a-b+1,a-c+1};\frac{-4z}{(1-z)^{2}}\right)}}$ \genhyperF{3}{2}@@{a,b,c}{a-b+1,a-c+1}{z} = (1-z)^{-a}\genhyperF{3}{2}@@{a-b-c+1,\frac{1}{2}a,\frac{1}{2}(a+1)}{a-b+1,a-c+1}{\frac{-4z}{(1-z)^{2}}}		hypergeom([a , b , c], [a - b + 1 , a - c + 1], z) = (1 - z)^(- a)* hypergeom([a - b - c + 1 ,(1)/(2)*a ,(1)/(2)*(a + 1)], [a - b + 1 , a - c + 1], (- 4*z)/((1 - z)^(2)))	HypergeometricPFQ[{a , b , c}, {a - b + 1 , a - c + 1}, z] == (1 - z)^(- a)* HypergeometricPFQ[{a - b - c + 1 ,Divide[1,2]*a ,Divide[1,2]*(a + 1)}, {a - b + 1 , a - c + 1}, Divide[- 4*z,(1 - z)^(2)]]	Failure	Failure	Failed [258 / 300] Result: -2.076719790+.860205503*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I} Result: -1.428233246+.1e-8*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2-1/2*I*3^(1/2)} ... skip entries to safe data	Skipped - Because timed out
16.6.E2	${\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a,2b-a-1,2-2b+a\atop b,a-b+\frac{3}{2}};\frac{z}{4}\right)=(1-z)^{-a}{{}_{3}F_{2}}\left({\frac{1}{3}a,\frac{1}{3}a+\frac{1}{3},\frac{1}{3}a+\frac{2}{3}\atop b,a-b+\frac{3}{2}};\frac{-27z}{4(1-z)^{3}}\right)}}$ \genhyperF{3}{2}@@{a,2b-a-1,2-2b+a}{b,a-b+\frac{3}{2}}{\frac{z}{4}} = (1-z)^{-a}\genhyperF{3}{2}@@{\frac{1}{3}a,\frac{1}{3}a+\frac{1}{3},\frac{1}{3}a+\frac{2}{3}}{b,a-b+\frac{3}{2}}{\frac{-27z}{4(1-z)^{3}}}		hypergeom([a , 2*b - a - 1 , 2 - 2*b + a], [b , a - b +(3)/(2)], (z)/(4)) = (1 - z)^(- a)* hypergeom([(1)/(3)*a ,(1)/(3)*a +(1)/(3),(1)/(3)*a +(2)/(3)], [b , a - b +(3)/(2)], (- 27*z)/(4*(1 - z)^(3)))	HypergeometricPFQ[{a , 2*b - a - 1 , 2 - 2*b + a}, {b , a - b +Divide[3,2]}, Divide[z,4]] == (1 - z)^(- a)* HypergeometricPFQ[{Divide[1,3]*a ,Divide[1,3]*a +Divide[1,3],Divide[1,3]*a +Divide[2,3]}, {b , a - b +Divide[3,2]}, Divide[- 27*z,4*(1 - z)^(3)]]	Failure	Failure	Failed [216 / 252] Result: .1888061791+.200959324e-1*I Test Values: {a = -3/2, b = -3/2, z = 1/2*3^(1/2)+1/2*I} Result: -.140210603-.95166922e-1*I Test Values: {a = -3/2, b = -3/2, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Skipped - Because timed out