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

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=45/8

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

Input Form

Hypergeometric2F1[-(39/8), 45/8, -(7/2), z] == (1/3845632) ((1/(1 + Sqrt[z])^(17/4)) (1922816 + 8171968 Sqrt[z] + 28344368 z + 73985496 z^(3/2) + 184503423 z^2 + 406920228 z^(5/2) + 935364144 z^3 + 2003299584 z^(7/2) + 5774216448 z^4 + 11538109440 z^(9/2) - 2930982912 z^5 - 48751312896 z^(11/2) - 75038785536 z^6 - 47501279232 z^(13/2) - 11176771584 z^7) + (1/(1 - Sqrt[z])^(17/4)) (1922816 - 8171968 Sqrt[z] + 28344368 z - 73985496 z^(3/2) + 184503423 z^2 - 406920228 z^(5/2) + 935364144 z^3 - 2003299584 z^(7/2) + 5774216448 z^4 - 11538109440 z^(9/2) - 2930982912 z^5 + 48751312896 z^(11/2) - 75038785536 z^6 + 47501279232 z^(13/2) - 11176771584 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]