A new class of generalized polynomials involving Laguerre and Euler polynomials

Year 2021, Volume: 50 Issue: 1, 1 - 13, 04.02.2021

Nabiullah Khan Talha Usman , Junesang Choi

https://doi.org/10.15672/hujms.555416

Cited By: 7

Abstract

Motivated by their importance and potential for applications in a variety of research fields, recently, numerous polynomials and their extensions have been introduced and investigated. In this paper, we modify the known generating functions of polynomials, due to both Milne-Thomsons and Dere-Simsek, to introduce a new class of polynomials and present some involved properties. As obvious special cases of the newly introduced polynomials, we also introduce power sum-Laguerre-Hermite polynomials and generalized Laguerre and Euler polynomials and give certain involved identities and formulas. We point out that our main results, being very general, are specialised to yield a number of known and new identities involving relatively simple and familiar polynomials.

Keywords

Milne-Thomsons polynomials, Dere-Simsek polynomials, Laguerre polynomials, Hermite polynomials, Euler polynomials, generalized Laguerre-Euler polynomials, summation formulae, symmetric identities

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