Regularized hypergeometric function 2F1: Identities (formula 07.24.17.0105)

Hypergeometric2F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1Regularized[a,b,c,z]

Identities

Functional identities

Quadratic transformations with fixed a,b,z

http://functions.wolfram.com/07.24.17.0105.01

Input Form

Hypergeometric2F1Regularized[a, b, 3/2, z] == (((Gamma[a - 1/2] Gamma[b - 1/2])/(2 Pi)) (Hypergeometric2F1Regularized[2 a - 1, 2 b - 1, a + b - 1/2, (1 + Sqrt[z])/2] - Hypergeometric2F1Regularized[2 a - 1, 2 b - 1, a + b - 1/2, (1 - Sqrt[z])/2]))/z^(1/2)

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]