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

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=-9/8

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

Input Form

Hypergeometric2F1[-(29/8), -(9/8), 23/4, z] == (1/(290504479719 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (535920 - 7065212 z + 46393823 z^2 - 219013771 z^3 + 1126704810 z^4 + 11784926414 z^5 + 5903144675 z^6 - 8076151 z^7 + 402132 z^8 + (1/Sqrt[1 - z]) (-535920 + 7333172 z - 49859439 z^2 + 241361026 z^3 - 1230833109 z^4 - 2168047456 z^5 + 2585018167 z^6 + 647365498 z^7 - 33410467 z^8 + 1608528 z^9)))

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]