Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bty5)

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=-7/8, b>=a

For fixed z and a=-7/8, b=45/8

http://functions.wolfram.com/07.23.03.bty5.01

Input Form

Hypergeometric2F1[-(7/8), 45/8, -(7/4), z] == (1/(55796 2^(3/4) (-1 + z)^6)) ((1 + Sqrt[1 - z])^(3/4) (2 (13949 - 41847 z + 406017 z^2 - 742289 z^3 + 649482 z^4 - 285312 z^5 + 50688 z^6) + (1/Sqrt[1 - z]) (27898 - 97643 z - 993371 z^2 + 2727535 z^3 - 3435779 z^4 + 2377312 z^5 - 876288 z^6 + 135168 z^7)))

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]