Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9j4)

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=-41/8, b>=a

For fixed z and a=-41/8, b=43/8

http://functions.wolfram.com/07.23.03.b9j4.01

Input Form

Hypergeometric2F1[-(41/8), 43/8, -(7/2), z] == (1/1021440) ((1/(1 + Sqrt[z])^(15/4)) (510720 + 1915200 Sqrt[z] + 6653040 z + 16609800 z^(3/2) + 42155091 z^2 + 91353900 z^(5/2) + 219550320 z^3 + 469497600 z^(7/2) + 1533692160 z^4 + 5095980032 z^(9/2) + 5306695680 z^5 - 7676231680 z^(11/2) - 21218263040 z^6 - 16511139840 z^(13/2) - 4402970624 z^7) + (1/(1 - Sqrt[z])^(15/4)) (510720 - 1915200 Sqrt[z] + 6653040 z - 16609800 z^(3/2) + 42155091 z^2 - 91353900 z^(5/2) + 219550320 z^3 - 469497600 z^(7/2) + 1533692160 z^4 - 5095980032 z^(9/2) + 5306695680 z^5 + 7676231680 z^(11/2) - 21218263040 z^6 + 16511139840 z^(13/2) - 4402970624 z^7))

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]