Regularized hypergeometric function 2F1: Representations through more general functions (formula 07.24.26.0102)

Hypergeometric2F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1Regularized[a,b,c,z]

Representations through more general functions

Through Meijer G

Classical cases involving products of ₂F^~₁ with linear arguments

http://functions.wolfram.com/07.24.26.0102.01

Input Form

(1/Sqrt[1 + z]) Hypergeometric2F1Regularized[a, b, 1/2 + a + b, -z] Hypergeometric2F1Regularized[1/2 + a, 1/2 + b, 3/2 + a + b, -z] == (2^(2 a + 2 b)/(Sqrt[Pi] Gamma[1 + 2 a] Gamma[1 + 2 b])) MeijerG[{{-2 a, -2 b, -a - b}, {}}, {{0}, {-(1/2) - a - b, -2 (a + 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

HypergeometricPFQRegularized[{},{b},z]
HypergeometricPFQRegularized[{a₁},{b₁},z]
HypergeometricPFQRegularized[{a₁,...,a_p},{b₁,...,b_q},z]