Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9eb)

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=35/8

http://functions.wolfram.com/07.23.03.b9eb.01

Input Form

Hypergeometric2F1[-(41/8), 35/8, -(11/2), z] == (1/15409152) ((1/(1 - Sqrt[z])^(19/4)) (7704576 - 36596736 Sqrt[z] + 100028160 z - 212094720 z^(3/2) + 384636000 z^2 - 628101012 z^(5/2) + 947974467 z^3 - 1345930740 z^(7/2) + 1813284000 z^4 - 2333041920 z^(9/2) + 2860805376 z^5 - 3330302976 z^(11/2) + 3505582080 z^6 - 2820014080 z^(13/2) + 1375928320 z^7 - 289669120 z^(15/2)) + (1/(1 + Sqrt[z])^(19/4)) (7704576 + 36596736 Sqrt[z] + 100028160 z + 212094720 z^(3/2) + 384636000 z^2 + 628101012 z^(5/2) + 947974467 z^3 + 1345930740 z^(7/2) + 1813284000 z^4 + 2333041920 z^(9/2) + 2860805376 z^5 + 3330302976 z^(11/2) + 3505582080 z^6 + 2820014080 z^(13/2) + 1375928320 z^7 + 289669120 z^(15/2)))

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]