Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bf4l)

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=7/8

http://functions.wolfram.com/07.23.03.bf4l.01

Input Form

Hypergeometric2F1[-(31/8), 7/8, 11/2, -z] == (1024 (Sqrt[z] Sqrt[1 + z] (1597120 + 13604040 z + 51586263 z^2 + 116002248 z^3 + 858375466 z^4 + 542522604 z^5 + 236055911 z^6 + 60728668 z^7 + 6966960 z^8) Cosh[ArcSinh[Sqrt[z]]/4] - (6388480 + 58808240 z + 243232107 z^2 + 601660059 z^3 + 1069410162 z^4 + 1103653174 z^5 + 653394911 z^6 + 265549375 z^7 + 64212148 z^8 + 6966960 z^9) Sinh[ArcSinh[Sqrt[z]]/4]))/(683050922697 z^(9/2) Sqrt[1 + z])

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]