DIFFERENTIAL EQUATIONS ASSOCIATED WITH MAHLER AND SHEFFER-MAHLER POLYNOMIALS

Abstract

In this paper, we study linear differential equations arising from the generating functions of Mahler and Sheffer-Mahler polynomials. We give explicit identities for the Mahler and Sheffer-Mahler polynomials. In addition, we investigate the zeros of the Sheffer-Mahler polynomials with numerical methods.