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

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=-15/8, b>=a

For fixed z and a=-15/8, b=5/8

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

Input Form

Hypergeometric2F1[-(15/8), 5/8, 21/4, z] == (1/(3204355 z^5)) (16 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (3120 - 21900 z + 67555 z^2 - 124813 z^3 + 240989 z^4 - 34307 z^5 + 4524 z^6 + (1/Sqrt[1 - z]) (-3120 + 23460 z - 78115 z^2 + 156048 z^3 - 296198 z^4 + 242788 z^5 - 50895 z^6 + 6032 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]