Generalized Laguerre function: Representations through more general functions (formula 07.03.26.0015)

LaguerreL

$Mathematica Notation$

Hypergeometric Functions

LaguerreL[nu,lambda,z]

Representations through more general functions

Through Meijer G

Classical cases involving ₁F^~₁

http://functions.wolfram.com/07.03.26.0015.01

Input Form

Hypergeometric1F1Regularized[-\[Nu], 1 + \[Lambda], -z] LaguerreL[\[Nu], \[Lambda], z] == (-(Sin[Pi \[Nu]]/(2^\[Lambda] Sqrt[Pi]))) MeijerG[{{1 + \[Nu], -\[Lambda] - \[Nu]}, {}}, {{0}, {-(\[Lambda]/2), (1 - \[Lambda])/2, -\[Lambda]}}, -(z^2/4)]

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

LaguerreL[n,z]
LaguerreL[nu,z]
LaguerreL[n,mu,z]