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

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=-39/8, b>=a

For fixed z and a=-39/8, b=37/8

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

Input Form

Hypergeometric2F1[-(39/8), 37/8, -(9/2), z] == (1/1247232) ((1/(1 - Sqrt[z])^(17/4)) (623616 - 2650368 Sqrt[z] + 7431424 z - 16509584 z^(3/2) + 32317948 z^2 - 57584865 z^(5/2) + 96953844 z^3 - 155661792 z^(7/2) + 245236992 z^4 - 379002624 z^(9/2) + 624239616 z^5 - 985780224 z^(11/2) + 1068367872 z^6 - 625016832 z^(13/2) + 147062784 z^7) + (1/(1 + Sqrt[z])^(17/4)) (623616 + 2650368 Sqrt[z] + 7431424 z + 16509584 z^(3/2) + 32317948 z^2 + 57584865 z^(5/2) + 96953844 z^3 + 155661792 z^(7/2) + 245236992 z^4 + 379002624 z^(9/2) + 624239616 z^5 + 985780224 z^(11/2) + 1068367872 z^6 + 625016832 z^(13/2) + 147062784 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]