Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9ju)

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.b9ju.01

Input Form

Hypergeometric2F1[-(41/8), 43/8, 5/2, z] == (1/(4424692545 z^(3/2))) (8 ((1 - Sqrt[z])^(9/4) (320620 + 721395 Sqrt[z] + 17634100 z + 315243120 z^(3/2) + 233176320 z^2 - 2963740416 z^(5/2) - 4233255936 z^3 + 6124584960 z^(7/2) + 12600606720 z^4 - 362086400 z^(9/2) - 9906683904 z^5 - 4402970624 z^(11/2)) - (1 + Sqrt[z])^(9/4) (320620 - 721395 Sqrt[z] + 17634100 z - 315243120 z^(3/2) + 233176320 z^2 + 2963740416 z^(5/2) - 4233255936 z^3 - 6124584960 z^(7/2) + 12600606720 z^4 + 362086400 z^(9/2) - 9906683904 z^5 + 4402970624 z^(11/2))))

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]