k-Oresme Polynomials and Their Derivatives

Abstract

In this study, we defined and studied k-Oresme polynomials using k-Oresme numbers and Oresme polynomials. We deduced some well-known properties and identities of this polynomials using some matrix methods and some combinatorial operations. Moreover, we examined the generating function of this family. Subsequently, we derived the derivatives of k-Oresme polynomials and we gave the generating function of this derivative sequence related to the generating function of k-Oresme polynomials. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.