Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bgz7)

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.bgz7.01

Input Form

Hypergeometric2F1[-(29/8), 29/8, -(7/2), z] == (1/(8960 (-1 + z)^3)) ((-8960 - 4240 z - 5019 z^2 - 9765 z^3 - 52416 z^4 + 347616 z^5 - 437376 z^6 + 163200 z^7) Cos[(3 ArcSin[Sqrt[z]])/4] + (1/Sqrt[1 - z]) (8 Sqrt[z] (-840 - 275 z - 336 z^2 - 756 z^3 - 22719 z^4 + 68238 z^5 - 64872 z^6 + 20400 z^7) 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]