Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5647)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=-11/3, b>=a

For fixed z and a=-11/3, b=-10/3

http://functions.wolfram.com/07.23.03.5647.01

Input Form

Hypergeometric2F1[-(11/3), -(10/3), 7/2, z] == (81 (-3 Sqrt[z] (98304 - 2392064 z - 403009439 z^2 - 752249945 z^3 + 543056984 z^4 + 562523360 z^5 + 51972800 z^6) Cos[ArcSin[Sqrt[z]]/3] + Sqrt[1 - z] (884736 - 21266432 z + 531005440 z^2 + 6075477919 z^3 + 9798182288 z^4 + 3492685760 z^5 + 206717120 z^6) Sin[ArcSin[Sqrt[z]]/3]))/(112435426285 Sqrt[1 - z] z^(5/2))

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]