Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5724)

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=-1/3

http://functions.wolfram.com/07.23.03.5724.01

Input Form

Hypergeometric2F1[-(11/3), -(1/3), 11/2, -z] == -((6561 (Sqrt[z] (207360 + 2411520 z + 13644288 z^2 + 54114304 z^3 - 484599919 z^4 - 496454693 z^5 + 35264290 z^6 + 4807736 z^7 + 362848 z^8) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[1 + z] (-622080 - 7050240 z - 38925824 z^2 - 151689216 z^3 - 716528640 z^4 + 1193122853 z^5 + 32996490 z^6 + 4626312 z^7 + 362848 z^8) Sinh[ArcSinh[Sqrt[z]]/3]))/(4834723330255 z^(9/2) Sqrt[1 + z]))

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]