Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5674)

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/07.23.03.5674.01

Input Form

Hypergeometric2F1[-(11/3), -(7/3), 9/2, -z] == -((243 (Sqrt[z] (221184 + 3776512 z + 38019072 z^2 - 2344631139 z^3 + 1126870007 z^4 + 2730131922 z^5 - 773293032 z^6 + 2539936 z^7) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[1 + z] (-663552 - 11132928 z - 110845952 z^2 - 1461526528 z^3 + 9460500769 z^4 - 8089973126 z^5 + 1174602920 z^6 + 2539936 z^7) Sinh[ArcSinh[Sqrt[z]]/3]))/ (690674761465 z^(7/2) 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]