Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5rm)

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=-47/8, b>=a

For fixed z and a=-47/8, b=45/8

http://functions.wolfram.com/07.23.03.b5rm.01

Input Form

Hypergeometric2F1[-(47/8), 45/8, 5/2, z] == (1/(11947740189 z^(3/2))) (8 ((1 + Sqrt[z])^(11/4) (670220 - 1843105 Sqrt[z] + 44234520 z + 629120624 z^(3/2) - 3167703616 z^2 - 2700208896 z^(5/2) + 24418279424 z^3 - 13181403136 z^(7/2) - 51391954944 z^4 + 58609565696 z^(9/2) + 18956681216 z^5 - 50624200704 z^(11/2) + 18408800256 z^6) - (1 - Sqrt[z])^(11/4) (670220 + 1843105 Sqrt[z] + 44234520 z - 629120624 z^(3/2) - 3167703616 z^2 + 2700208896 z^(5/2) + 24418279424 z^3 + 13181403136 z^(7/2) - 51391954944 z^4 - 58609565696 z^(9/2) + 18956681216 z^5 + 50624200704 z^(11/2) + 18408800256 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]