Generalized Hypergeometric Functions & Meijer G -Function - 16.6 Transformations of Variable
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
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| 16.6.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}}}}
\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}}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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)))
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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)]]
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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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}}}}
\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}}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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)))
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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)]]
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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 |