Regularized hypergeometric function 2F1: Representations through more general functions (formula 07.24.26.0036)

Hypergeometric2F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1Regularized[a,b,c,z]

Representations through more general functions

Through Meijer G

Classical cases involving algebraic functions with squares in arguments

http://functions.wolfram.com/07.24.26.0036.01

Input Form

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