A new class of generalized polynomials involving Laguerre and Euler polynomials

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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