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

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=-29/8, b>=a

For fixed z and a=-29/8, b=-19/8

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

Input Form

Hypergeometric2F1[-(29/8), -(19/8), 5/2, z] == (1/(37272075 z^(3/2))) (16 ((-Sqrt[z]) (21489 - 3181454 z - 17550802 z^2 - 15636384 z^3 - 2018503 z^4 + 27094 z^5) Cos[(3 ArcSin[Sqrt[z]])/4] - (1/Sqrt[1 - z]) (2 (-14326 + 580203 z + 5430939 z^2 + 842846 z^3 - 5837184 z^4 - 1016025 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]