Regularized hypergeometric function 2F1: Representations through more general functions (formula 07.24.26.0160)

Hypergeometric2F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1Regularized[a,b,c,z]

Representations through more general functions

Through Meijer G

Classical cases involving algebraic functions and ₂F₁with linear arguments

http://functions.wolfram.com/07.24.26.0160.01

Input Form

Sqrt[1 + z] Hypergeometric2F1Regularized[a, b, a + b + 1/2, -z] Hypergeometric2F1[1 - a, 1 - b, 3/2 - a - b, -z] == ((Cos[(-a + b) Pi] Gamma[3/2 - a - b])/Pi^(3/2)) MeijerG[{{1/2, 1/2 - a + b, 1/2 + a - b}, {}}, {{0}, {-(1/2) + a + b, 1/2 - 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]