Regularized hypergeometric function 2F1: Representations through more general functions (formula 07.24.26.0092)

Hypergeometric2F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1Regularized[a,b,c,z]

Representations through more general functions

Through Meijer G

Classical cases involving powers of ₂F^~₁

http://functions.wolfram.com/07.24.26.0092.01

Input Form

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