Regularized hypergeometric function 2F1: Identities (formula 07.24.17.0100)

Hypergeometric2F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1Regularized[a,b,c,z]

Identities

Functional identities

Quadratic transformations with fixed a,b,z

http://functions.wolfram.com/07.24.17.0100.01

Input Form

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