Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bc2k)

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=-37/8, b>=a

For fixed z and a=-37/8, b=31/8

http://functions.wolfram.com/07.23.03.bc2k.01

Input Form

Hypergeometric2F1[-(37/8), 31/8, 19/4, z] == (1/(11364965919 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (2148146 + 683501 z + 1841268 z^2 + 11507925 z^3 - 108053716 z^4 + 248591052 z^5 - 260514144 z^6 + 132008448 z^7 - 26357760 z^8) + (1/Sqrt[1 - z]) (-8592584 + 1562288 z - 4923997 z^2 - 41470377 z^3 + 1166968241 z^4 - 4194696115 z^5 + 6686530848 z^6 - 5585724672 z^7 + 2402070528 z^8 - 421724160 z^9)))

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]