Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.6167)

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=-8/3, b>=a

For fixed z and a=-8/3, b=-4/3

http://functions.wolfram.com/07.23.03.6167.01

Input Form

Hypergeometric2F1[-(8/3), -(4/3), 11/2, z] == -((6561 (Sqrt[z] (165888 - 2039808 z + 12486656 z^2 - 55889920 z^3 - 834250195 z^4 + 505489831 z^5 + 372041884 z^6 + 1995664 z^7) Cos[ArcSin[Sqrt[z]]/3] + Sqrt[1 - z] (-497664 + 5971968 z - 35756032 z^2 + 157822976 z^3 - 928657408 z^4 - 2475135473 z^5 - 601543244 z^6 + 1995664 z^7) Sin[ArcSin[Sqrt[z]]/3]))/ (7597422376115 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]