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

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=-31/8, b>=a

For fixed z and a=-31/8, b=45/8

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

Input Form

Hypergeometric2F1[-(31/8), 45/8, 9/2, z] == (1/(377207225967 z^(7/2))) (128 ((1 + Sqrt[z])^(11/4) (228160 - 627440 Sqrt[z] + 2606728 z - 5795977 z^(3/2) + 19550460 z^2 - 41411040 z^(5/2) + 210819840 z^3 + 981350656 z^(7/2) - 4754207744 z^4 + 3447009280 z^(9/2) + 5716705280 z^5 - 8762490880 z^(11/2) + 3186360320 z^6) - (1 - Sqrt[z])^(11/4) (228160 + 627440 Sqrt[z] + 2606728 z + 5795977 z^(3/2) + 19550460 z^2 + 41411040 z^(5/2) + 210819840 z^3 - 981350656 z^(7/2) - 4754207744 z^4 - 3447009280 z^(9/2) + 5716705280 z^5 + 8762490880 z^(11/2) + 3186360320 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]