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

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=-31/8, b>=a

For fixed z and a=-31/8, b=47/8

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

Input Form

Hypergeometric2F1[-(31/8), 47/8, 7/2, -z] == (1/(1796067 z^(5/2))) (64 (2 Sqrt[z] (2 - 29 z + 14711 z^2 + 102176 z^3 + 239472 z^4 + 232704 z^5 + 80640 z^6) Cosh[ArcSinh[Sqrt[z]]/4] - (1/Sqrt[1 + z]) ((16 - 221 z + 5273 z^2 + 94518 z^3 + 395728 z^4 + 691488 z^5 + 546048 z^6 + 161280 z^7) Sinh[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]