Gauss hypergeometric function 2F1: Representations through more general functions (formula 07.23.26.0055)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Representations through more general functions

Through Meijer G

Classical cases involving algebraic functions with cubics in arguments

http://functions.wolfram.com/07.23.26.0055.01

Input Form

((9 + 8 z) Hypergeometric2F1[a, 1/3 + a, 3/2, (z (9 + 8 z)^2)/(3 + 4 z)^3])/ (3 + 4 z)^(3 a) == ((Sqrt[Pi] 3^(2 - 3 a))/(2 Gamma[4/3 - a] Gamma[-1 + 3 a])) MeijerG[{{-(1/3) + a, 2 - 3 a}, {}}, {{0}, {-(1/2)}}, z] /; Abs[z] < 1 || Re[z] >= 0

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)

2001-10-29

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]