Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bgk8)

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=5/8

http://functions.wolfram.com/07.23.03.bgk8.01

Input Form

Hypergeometric2F1[-(29/8), 5/8, -(11/2), z] == (1/(135168 (1 - z)^(5/2))) (Sqrt[1 - z] (135168 - 252672 z + 99680 z^2 + 11193 z^3 + 4855 z^4 + 3180 z^5 + 3120 z^6) Cos[(3 ArcSin[Sqrt[z]])/4] + Sqrt[z] (101376 - 204288 z + 93156 z^2 + 8173 z^3 + 2875 z^4 + 1620 z^5 + 3120 z^6) Sin[(3 ArcSin[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]