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

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=27/8, b>=a

For fixed z and a=27/8, b=37/8

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

Input Form

Hypergeometric2F1[27/8, 37/8, -(3/2), z] == -((1/(8816 (1 - z)^(19/2))) (Sqrt[1 - z] (-8816 + 173565 z - 3448158 z^2 - 24010826 z^3 - 20470080 z^4 - 2397819 z^5 + 27094 z^6) Cos[(3 ArcSin[Sqrt[z]])/4] + 2 Sqrt[z] (-3306 + 65569 z - 4155893 z^2 - 16643246 z^3 - 11494348 z^4 - 1205683 z^5 + 13547 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]