Regularized hypergeometric function 2F1: Representations through more general functions (formula 07.24.26.0038)

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/07.24.26.0038.01

Input Form

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