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

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=-21/8, b>=a

For fixed z and a=-21/8, b=29/8

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

Input Form

Hypergeometric2F1[-(21/8), 29/8, -(5/2), -z] == (1/(320 (1 + z)^(7/2))) ((-Sqrt[1 + z]) (-320 + 168 z - 259 z^2 + 1197 z^3 + 7416 z^4 + 8976 z^5 + 3264 z^6) Cosh[(3 ArcSinh[Sqrt[z]])/4] + Sqrt[z] (-240 + 91 z - 154 z^2 + 3987 z^3 + 11496 z^4 + 10608 z^5 + 3264 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]