Regularized hypergeometric function 2F1: Identities (formula 07.24.17.0073)

Hypergeometric2F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1Regularized[a,b,c,z]

Identities

Functional identities

Relations including three Kummer's solutions

http://functions.wolfram.com/07.24.17.0073.01

Input Form

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