A new class of generalized polynomials associated with Laguerre and Bernoulli polynomials

Abstract

Motivated by their importance and potential for applications in certain problems in number theory, combinatorics,classical and numerical analysis, and other fields of applied mathematics, a variety of polynomials and numberswith their variants and extensions have recently been introduced and investigated. In this paper, we aim to introducegeneralized Laguerre–Bernoulli polynomials and investigate some of their properties such as explicit summation formulas,addition formulas, implicit formulas, and symmetry identities. Relevant connections of the results presented here withthose relatively simple numbers and polynomials are considered.