d-Oresme Polynomials and Their Matrix Representations

Abstract

In this paper, we define the concept of d-Oresme polynomials, which is a generalization of the classical Oresme polynomials. We obtain several fundamental properties for these new polynomials including the generating function, the Binet-like formula, combinatorial identities and summation formulas. Then, we introduce the infinite d- Oresme polynomials matrix, which is a Riordan matrix. We present two new factorizations of the infinite Pascal matrix including the d-Oresme polynomials by Riordan method.