Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9iv)

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.b9iv.01

Input Form

Hypergeometric2F1[-(41/8), 43/8, -(11/2), z] == (1/107864064) ((1/(1 - Sqrt[z])^(23/4)) (53932032 - 310109184 Sqrt[z] + 1006629120 z - 2473825536 z^(3/2) + 5111017632 z^2 - 9370781532 z^(5/2) + 15708425997 z^3 - 24542523060 z^(7/2) + 36142196112 z^4 - 50536721664 z^(9/2) + 67175716608 z^5 - 84659807232 z^(11/2) + 98156298240 z^6 - 93939695616 z^(13/2) + 63394086912 z^7 - 25317081088 z^(15/2) + 4402970624 z^8) + (1/(1 + Sqrt[z])^(23/4)) (53932032 + 310109184 Sqrt[z] + 1006629120 z + 2473825536 z^(3/2) + 5111017632 z^2 + 9370781532 z^(5/2) + 15708425997 z^3 + 24542523060 z^(7/2) + 36142196112 z^4 + 50536721664 z^(9/2) + 67175716608 z^5 + 84659807232 z^(11/2) + 98156298240 z^6 + 93939695616 z^(13/2) + 63394086912 z^7 + 25317081088 z^(15/2) + 4402970624 z^8))

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]