Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bc40)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-37/8, b>=a

For fixed z and a=-37/8, b=33/8

http://functions.wolfram.com/07.23.03.bc40.01

Input Form

Hypergeometric2F1[-(37/8), 33/8, 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (457080832 - 712403328 z - 508817673 z^2 - 583026353 z^3 - 1273362363 z^4 + 31264952733 z^5 - 75243593432 z^6 + 77177269488 z^7 - 37658884032 z^8 + 7210038528 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (457080832 - 712403328 z - 508817673 z^2 - 583026353 z^3 - 1273362363 z^4 + 31264952733 z^5 - 75243593432 z^6 + 77177269488 z^7 - 37658884032 z^8 + 7210038528 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (457080832 - 998078848 z - 110434233 z^2 - 213935813 z^3 - 835921723 z^4 + 7684168233 z^5 - 15641180912 z^6 + 14573733248 z^7 - 6634121472 z^8 + 1201673088 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (457080832 - 712403328 z - 508817673 z^2 - 583026353 z^3 - 1273362363 z^4 + 31264952733 z^5 - 75243593432 z^6 + 77177269488 z^7 - 37658884032 z^8 + 7210038528 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (6415316309677275 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^5)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]