Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6nh)

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=-45/8, b>=a

For fixed z and a=-45/8, b=7/8

http://functions.wolfram.com/07.23.03.b6nh.01

Input Form

Hypergeometric2F1[-(45/8), 7/8, 11/4, z] == (1/(27041883 z^2)) (2 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-418470 + 3626740 z - 2574244 z^2 + 3700784 z^3 - 3349254 z^4 + 1860908 z^5 - 582400 z^6 + 78848 z^7 + (1/Sqrt[1 - z]) (418470 - 3835975 z + 11095776 z^2 - 19618130 z^3 + 23487426 z^4 - 18335887 z^5 + 9019360 z^6 - 2546432 z^7 + 315392 z^8)))

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]