Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5rc)

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=-47/8, b>=a

For fixed z and a=-47/8, b=45/8

http://functions.wolfram.com/07.23.03.b5rc.01

Input Form

Hypergeometric2F1[-(47/8), 45/8, 1/2, z] == (1/36818922) ((1/(1 - Sqrt[z])^(1/4)) (18409461 + 82987011 Sqrt[z] - 1240373544 z - 1627435024 z^(3/2) + 13688266816 z^2 + 8953174272 z^(5/2) - 55681196032 z^3 - 20134510592 z^(7/2) + 102997426176 z^4 + 19834535936 z^(9/2) - 88228757504 z^5 - 7112491008 z^(11/2) + 28449964032 z^6) + (1/(1 + Sqrt[z])^(1/4)) (18409461 - 82987011 Sqrt[z] - 1240373544 z + 1627435024 z^(3/2) + 13688266816 z^2 - 8953174272 z^(5/2) - 55681196032 z^3 + 20134510592 z^(7/2) + 102997426176 z^4 - 19834535936 z^(9/2) - 88228757504 z^5 + 7112491008 z^(11/2) + 28449964032 z^6))

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]