Regularized hypergeometric function 2F1: Identities (formula 07.24.17.0057)

Hypergeometric2F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1Regularized[a,b,c,z]

Identities

Functional identities

Major general cases

http://functions.wolfram.com/07.24.17.0057.01

Input Form

Hypergeometric2F1Regularized[a, b, c, z] == Pi Csc[Pi (c - a - b)] ((1/(Gamma[c - a] Gamma[c - b])) Hypergeometric2F1Regularized[a, b, a + b - c + 1, 1 - z] - (1/(Gamma[a] Gamma[b])) (1 - z)^(c - a - b) Hypergeometric2F1Regularized[c - a, c - b, 1 - a - b + c, 1 - z]) /; !Element[c - a - b, Integers]

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]