Regularized confluent hypergeometric function 1F1: Representations through more general functions (formula 07.21.26.0050)

Hypergeometric1F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric1F1Regularized[a,b,z]

Representations through more general functions

Through Meijer G

Generalized cases involving exp and products of ₁F^~₁

http://functions.wolfram.com/07.21.26.0050.01

Input Form

(Hypergeometric1F1Regularized[a, 2 a, z] Hypergeometric1F1Regularized[c, 2 c, z])/E^z == ((2^(1 - a - c) Sqrt[Pi])/(Gamma[a] Gamma[c])) MeijerG[{{1 - (a + c)/2, (1 - a - c)/2}, {}}, {{0}, {1 - a - c, 1/2 - c, 1/2 - a}}, (I z)/2, 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)

2007-05-02

HypergeometricPFQRegularized[{},{b},z]
HypergeometricPFQRegularized[{a₁,a₂},{b₁},z]
HypergeometricPFQRegularized[{a₁,...,a_p},{b₁,...,b_q},z]