Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b73a)

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=-45/8, b>=a

For fixed z and a=-45/8, b=33/8

http://functions.wolfram.com/07.23.03.b73a.01

Input Form

Hypergeometric2F1[-(45/8), 33/8, 5, z] == (65536 2^(1/4) (-4 Sqrt[1 - z] (21425664 + 20309744 z + 34467979 z^2 + 135040269 z^3 - 6249427451 z^4 + 23139824291 z^5 - 37360647264 z^6 + 31470313776 z^7 - 13618961664 z^8 + 2403346176 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 2 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (21425664 + 20309744 z + 34467979 z^2 + 135040269 z^3 - 6249427451 z^4 + 23139824291 z^5 - 37360647264 z^6 + 31470313776 z^7 - 13618961664 z^8 + 2403346176 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (42851328 + 13837408 z + 39154843 z^2 + 220770823 z^3 - 3355076167 z^4 + 10357499357 z^5 - 15044032648 z^6 + 11736428592 z^7 - 4778081088 z^8 + 801115392 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 2 Sqrt[1 - z] (21425664 + 20309744 z + 34467979 z^2 + 135040269 z^3 - 6249427451 z^4 + 23139824291 z^5 - 37360647264 z^6 + 31470313776 z^7 - 13618961664 z^8 + 2403346176 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (305491252841775 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^4)

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]