Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b56x)

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=13/8

http://functions.wolfram.com/07.23.03.b56x.01

Input Form

Hypergeometric2F1[-(47/8), 13/8, -(23/4), z] == (1/(1538240 2^(3/4) (-1 + z))) ((1 + Sqrt[1 - z])^(3/4) (-769120 - 652080 z - 605990 z^2 - 596409 z^3 - 622944 z^4 - 718080 z^5 + 5271552 z^6 + (1/Sqrt[1 - z]) (2 (-384560 - 133760 z - 91905 z^2 - 81917 z^3 - 89096 z^4 - 123840 z^5 - 3480576 z^6 + 3514368 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]