Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bv3j)

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=-5/8, b>=a

For fixed z and a=-5/8, b=37/8

http://functions.wolfram.com/07.23.03.bv3j.01

Input Form

Hypergeometric2F1[-(5/8), 37/8, -(3/2), z] == -((1/(18096 (1 - z)^(11/2))) (Sqrt[1 - z] (-18096 + 60697 z + 52780 z^2 - 177443 z^3 + 199614 z^4 - 104208 z^5 + 21216 z^6) Cos[(3 ArcSin[Sqrt[z]])/4] + 2 Sqrt[z] (-6786 + 23751 z + 61117 z^2 - 132775 z^3 + 124533 z^4 - 57408 z^5 + 10608 z^6) Sin[(3 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]