Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bfn6)

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=-31/8, b>=a

For fixed z and a=-31/8, b=37/8

http://functions.wolfram.com/07.23.03.bfn6.01

Input Form

Hypergeometric2F1[-(31/8), 37/8, 13/4, z] == (1/(64378405 z^3)) (4 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (14260 + 163277 z + 5708991 z^2 - 43108368 z^3 + 97383552 z^4 - 88897536 z^5 + 28753920 z^6 + (1/Sqrt[1 - z]) (-14260 - 156147 z - 5625570 z^2 + 54031465 z^3 - 165104352 z^4 + 229807872 z^5 - 151277568 z^6 + 38338560 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]