Certain Laguerre-based Generalized Apostol Type Polynomials

Authors

DOI:

https://doi.org/10.5556/j.tkjm.53.2022.3491

Keywords:

Laguerre polynomials, Hermite polynomials, Hermite-based generalized Apostol type polynomials, Laguerre-based generalized Apostol type polynomials, implicit formula, summation formulae, symmetric identities

Abstract

A variety of polynomials, their extensions and variants have been extensively investigated, due mainly to their potential applications in diverse research areas. In this paper, we aim to introduce Laguerre-based generalized Apostol type polynomials and investigate some properties and identities involving them. Among them, some differential-recursive relations for the Hermite-Laguerre polynomials, which are expressed in terms of generalized Apostol type numbers and the Laguerre-based generalized Apostol type polynomials, an implicit summation formula and addition-symmetry identities for the Laguerre-based generalized Apostol type polynomials are presented. The results presented here, being very general, are pointed out to reduce to yield some known or new formulas and identities for relatively simple polynomials and numbers.

Author Biography

Junesang Choi, Dongguk University

Full Professor

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Published

2021-04-08 — Updated on 2022-01-18

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How to Cite

Choi, J., Khan, N., & Usman, T. (2022). Certain Laguerre-based Generalized Apostol Type Polynomials. Tamkang Journal of Mathematics, 53(1), 59-74. https://doi.org/10.5556/j.tkjm.53.2022.3491 (Original work published April 8, 2021)

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