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

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=29/8

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

Input Form

Hypergeometric2F1[-(29/8), 29/8, -(5/2), z] == (1/(320 (-1 + z)^2)) (4 (80 + 238 z + 861 z^2 + 7098 z^3 - 59772 z^4 + 92208 z^5 - 40800 z^6) Cos[(3 ArcSin[Sqrt[z]])/4] - (1/Sqrt[1 - z]) (Sqrt[z] (-240 - 679 z - 2457 z^2 - 112032 z^3 + 403104 z^4 - 450432 z^5 + 163200 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]