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

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.basm.01

Input Form

Hypergeometric2F1[-(39/8), 45/8, 7/2, z] == (1/(11947740189 z^(5/2))) (32 ((1 + Sqrt[z])^(11/4) (34224 - 94116 Sqrt[z] + 702305 z - 1725460 z^(3/2) + 16940880 z^2 + 143821568 z^(5/2) - 689151232 z^3 + 76200960 z^(7/2) + 2497003520 z^4 - 2458255360 z^(9/2) - 1503068160 z^5 + 3013345280 z^(11/2) - 1095761920 z^6) + (1 - Sqrt[z])^(11/4) (-34224 - 94116 Sqrt[z] - 702305 z - 1725460 z^(3/2) - 16940880 z^2 + 143821568 z^(5/2) + 689151232 z^3 + 76200960 z^(7/2) - 2497003520 z^4 - 2458255360 z^(9/2) + 1503068160 z^5 + 3013345280 z^(11/2) + 1095761920 z^6)))

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]