Abstract
The aim of this paper is to introduce the degenerate generalized Laguerre polynomials as the degenerate version of the generalized Laguerre polynomials and to derive some properties related to those polynomials and Lah numbers, including an explicit expression, a Rodrigues type formula, and expressions for the derivatives. The novelty of the present paper is that it is the first paper on degenerate versions of orthogonal polynomials.
Highlights
1 Introduction The generalized Laguerre polynomials are classical orthogonal polynomials which are orthogonal with respect to the gamma distribution e–xxα dx on the interval (0, ∞)
The generalized Laguerre polynomials are widely used in many problems of quantum mechanics, mathematical physics and engineering
Vibronic transitions in the Franck–Condon approximation can be described by using Laguerre polynomials [6]
Summary
The generalized Laguerre polynomials are classical orthogonal polynomials which are orthogonal with respect to the gamma distribution e–xxα dx on the interval (0, ∞). The generalized Laguerre polynomials are widely used in many problems of quantum mechanics, mathematical physics and engineering. The radial part of the wave function is a generalized Laguerre polynomial [14]. We obtain an explicit formula and a Rodrigues type formula for the degenerate Laguerre polynomials.
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