Gauss hypergeometric function 2F1: Representations through more general functions (formula 07.23.26.0034)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Representations through more general functions

Through Meijer G

Classical cases involving algebraic functions with quadratic arguments

http://functions.wolfram.com/07.23.26.0034.01

Input Form

((1 + Sqrt[z])^(2 (a - 2 b)) Hypergeometric2F1[a, b, 2 b, -((4 Sqrt[z])/(-1 + Sqrt[z])^2)])/((-1 + Sqrt[z])^2/(1 + Sqrt[z])^2)^b == (1/Gamma[-a + 2 b]) Gamma[1/2 + a - b] Gamma[1/2 + b] MeijerG[{{1 + a - 2 b}, {1/2 + a - b}}, {{0}, {1/2 - b}}, 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)

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]