Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.beu0)

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=-17/8

http://functions.wolfram.com/07.23.03.beu0.01

Input Form

Hypergeometric2F1[-(31/8), -(17/8), 9/2, -z] == -((256 (Sqrt[z] Sqrt[1 + z] (-11408 - 187519 z - 1831697 z^2 - 803958980 z^3 + 1545466974 z^4 - 491878743 z^5 + 9582963 z^6 + 251082 z^7) Cosh[ArcSinh[Sqrt[z]]/4] + 2 (22816 + 390724 z + 3919361 z^2 + 50266500 z^3 - 154778735 z^4 - 94976796 z^5 + 101788275 z^6 - 4854252 z^7 - 125541 z^8) Sinh[ArcSinh[Sqrt[z]]/4]))/(199697943159 z^(7/2) 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]