Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5n9)

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=39/8

http://functions.wolfram.com/07.23.03.b5n9.01

Input Form

Hypergeometric2F1[-(47/8), 39/8, -(11/2), z] == (1/(946176 (1 - z)^(9/2))) (Sqrt[1 - z] (946176 + 1112832 z + 1602720 z^2 + 2773639 z^3 + 6140310 z^4 + 20225975 z^5 + 172455932 z^6 - 1352965680 z^7 + 2560326912 z^8 - 1938182400 z^9 + 525837312 z^10) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (236544 + 204288 z + 282324 z^2 + 512941 z^3 + 1231318 z^4 + 4430173 z^5 + 629493788 z^6 - 2423721168 z^7 + 3463688448 z^8 - 2201101056 z^9 + 525837312 z^10) Sin[ArcSin[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]