A note on degenerate generalized Laguerre polynomials and Lah numbers

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 expressi...

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Bibliographic Details
Published in:Advances in difference equations 2021-09, Vol.2021 (1), p.1-12, Article 421
Main Authors: Kim, Taekyun, Dolgy, Dmitry V., Kim, Dae San, Kim, Hye Kyung, Park, Seong Ho
Format: Article
Language:English
Subjects:
Analysis
Degenerate exponential function
Degenerate generalized Laguerre polynomials
Difference and Functional Equations
Difference Equations
Functional Analysis
Lah numbers
Mathematics
Mathematics and Statistics
Numbers
Ordinary Differential Equations
Partial Differential Equations
Polynomials
Quantum physics
Random variables
Special Functions and Orthogonal Polynomials
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Summary: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.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-021-03574-8