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

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=-29/8, b>=a

For fixed z and a=-29/8, b=45/8

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

Input Form

Hypergeometric2F1[-(29/8), 45/8, -(1/2), -z] == (1/(148 (1 + z)^(5/2))) (-2 Sqrt[1 + z] (-74 + 2849 z + 72205 z^2 + 372064 z^3 + 750800 z^4 + 659200 z^5 + 211200 z^6) Cosh[(3 ArcSinh[Sqrt[z]])/4] + Sqrt[z] (-111 + 38787 z + 394674 z^2 + 1356528 z^3 + 2108000 z^4 + 1529600 z^5 + 422400 z^6) 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]