Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5lg)

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=37/8

http://functions.wolfram.com/07.23.03.b5lg.01

Input Form

Hypergeometric2F1[-(47/8), 37/8, -(11/2), z] == (1/18292736) ((1/(1 - Sqrt[z])^(17/4)) (9146368 - 38872064 Sqrt[z] + 108353280 z - 239416576 z^(3/2) + 464548448 z^2 - 819916188 z^(5/2) + 1360488571 z^3 - 2147399540 z^(7/2) + 3285021168 z^4 - 4890938624 z^(9/2) + 7230775552 z^5 - 10612073472 z^(11/2) + 16646389760 z^6 - 25417351168 z^(13/2) + 27169849344 z^7 - 15833759744 z^(15/2) + 3725590528 z^8) + (1/(1 + Sqrt[z])^(17/4)) (9146368 + 38872064 Sqrt[z] + 108353280 z + 239416576 z^(3/2) + 464548448 z^2 + 819916188 z^(5/2) + 1360488571 z^3 + 2147399540 z^(7/2) + 3285021168 z^4 + 4890938624 z^(9/2) + 7230775552 z^5 + 10612073472 z^(11/2) + 16646389760 z^6 + 25417351168 z^(13/2) + 27169849344 z^7 + 15833759744 z^(15/2) + 3725590528 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]