Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9j5)

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.b9j5.01

Input Form

Hypergeometric2F1[-(41/8), 43/8, -(7/2), -z] == (1/(510720 (1 + z)^(23/8))) ((510720 - 3333360 z + 15588531 z^2 - 78997611 z^3 + 814247280 z^4 + 3351572224 z^5 - 559104000 z^6 - 7401046016 z^7 - 4402970624 z^8) Cos[(7 ArcTan[Sqrt[z]])/4] + 2 Sqrt[z] (446880 - 2609460 z + 11826759 z^2 - 60875430 z^3 + 1249046656 z^4 + 6596821504 z^5 + 9124577280 z^6 + 3852599296 z^7) Sin[(7 ArcTan[Sqrt[z]])/4])

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]