Regularized hypergeometric function 2F1: Representations through more general functions (formula 07.24.26.0028)

Hypergeometric2F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1Regularized[a,b,c,z]

Representations through more general functions

Through Meijer G

Classical cases involving algebraic functions with quadratic arguments

http://functions.wolfram.com/07.24.26.0028.01

Input Form

(1 + z)^(1 + 2 a - 2 c) ((-1 + z)^2/(1 + z)^2)^(1/2 + 2 a - c) Hypergeometric2F1Regularized[a, 1/2 + a, c, (4 z)/(1 + z)^2] == (Gamma[1 + 2 a - c]/Gamma[-1 - 2 a + 2 c]) MeijerG[{{2 (1 + a - c)}, {1 + 2 a - c}}, {{0}, {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]