Regularized hypergeometric function 2F1: Representations through more general functions (formula 07.24.26.0011)

Hypergeometric2F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1Regularized[a,b,c,z]

Representations through more general functions

Through Meijer G

Classical cases for the direct function itself

http://functions.wolfram.com/07.24.26.0011.01

Input Form

Hypergeometric2F1Regularized[a, b, c, z] == 1/Gamma[c] - (Pi/(Gamma[a] Gamma[b])) MeijerG[{{1, 1 - a, 1 - b}, {1/2}}, {{1}, {0, 1/2, 1 - c}}, z] /; Abs[z] < 1

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]