Special functions MOC

Associated Laguerre polynomial

The associated Laguerre polynomials (also called generalized Laguerre polynomials) are polynomials of degree defined (by one convention¹) for as fun

where is a Laguerre polynomial, or equivalently,

Mathematica

The associated Laguerre polynomial may be generated in Wolfram Mathematica with LaguerreL[p,q,x].

Properties

1. Clearly .

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Footnotes

1. 2018. Introduction to quantum mechanics, §4.2, pp. 149–150 ↩