Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bv91)

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=-5/8, b>=a

For fixed z and a=-5/8, b=45/8

http://functions.wolfram.com/07.23.03.bv91.01

Input Form

Hypergeometric2F1[-(5/8), 45/8, -(11/2), -z] == (1/(338415616 (1 + z)^(21/2))) ((-Sqrt[1 + z]) (-338415616 - 3263018752 z - 13869512160 z^2 - 33635565987 z^3 - 49277511051 z^4 - 38012224614 z^5 + 16569431242 z^6 + 27110844625 z^7 + 19651461441 z^8 + 8362046888 z^9 + 2009370896 z^10 + 211778112 z^11) Cosh[(3 ArcSinh[Sqrt[z]])/4] + Sqrt[z] (-253811712 - 2484278272 z - 10735892916 z^2 - 26537098005 z^3 - 39835396469 z^4 - 32164190058 z^5 + 28118348562 z^6 + 36008632583 z^7 + 23594549655 z^8 + 9340260072 z^9 + 2115259952 z^10 + 211778112 z^11) Sinh[(3 ArcSinh[Sqrt[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]