Regularized hypergeometric function 2F1: Representations through more general functions (formula 07.24.26.0220)

Hypergeometric2F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1Regularized[a,b,c,z]

Representations through more general functions

Through Meijer G

Generalized cases involving algebraic functions with squares in arguments

http://functions.wolfram.com/07.24.26.0220.01

Input Form

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

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]