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

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=-23/8, b>=a

For fixed z and a=-23/8, b=37/8

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

Input Form

Hypergeometric2F1[-(23/8), 37/8, 1/2, z] == (1/14326) ((1/(1 + Sqrt[z])^(5/4)) (7163 - 13040 Sqrt[z] - 216864 z - 63360 z^(3/2) + 864000 z^2 + 571392 z^(5/2) - 798720 z^3 - 638976 z^(7/2)) + (1/(1 - Sqrt[z])^(5/4)) (7163 + 13040 Sqrt[z] - 216864 z + 63360 z^(3/2) + 864000 z^2 - 571392 z^(5/2) - 798720 z^3 + 638976 z^(7/2)))

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]