A new class of generalized polynomials involving Laguerre and Euler polynomials

Authors : Nabiullah KHAN, Talha USMAN, Junesang CHOİ

Pages : 1-13

Doi:10.15672/hujms.555416

View : 24 | Download : 10

Publication Date : 2021-02-04

Article Type : Research Paper

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