Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5675)

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=-7/3

http://functions.wolfram.com/07.23.03.5675.01

Input Form

Hypergeometric2F1[-(11/3), -(7/3), 11/2, z] == -((6561 (Sqrt[z] (663552 - 10813440 z + 92094464 z^2 - 615677952 z^3 - 24215121351 z^4 - 4782869959 z^5 + 24037395510 z^6 + 5479452408 z^7 + 14876768 z^8) Cos[ArcSin[Sqrt[z]]/3] + Sqrt[1 - z] (-1990656 + 31850496 z - 267108352 z^2 + 1771929600 z^3 - 17499660288 z^4 - 91330419181 z^5 - 65315389218 z^6 - 8157270648 z^7 + 14876768 z^8) Sin[ArcSin[Sqrt[z]]/3]))/(198223656540455 Sqrt[1 - z] z^(9/2)))

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]