Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bf8l)

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=-31/8, b>=a

For fixed z and a=-31/8, b=15/8

http://functions.wolfram.com/07.23.03.bf8l.01

Input Form

Hypergeometric2F1[-(31/8), 15/8, -(9/2), z] == (1/(21504 (1 - z)^(5/2))) (2 Sqrt[1 - z] (10752 - 4480 z - 3450 z^2 - 3687 z^3 - 4961 z^4 - 12320 z^5 + 16720 z^6) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (5376 - 3920 z - 1739 z^2 - 1423 z^3 - 1782 z^4 - 41360 z^5 + 33440 z^6) 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]