Derivative formulas related to unification of generating functions for sheffer type sequences

Abstract

The main aim of this paper is to present partial derivative formulas for an unification, which was introduced by the author in "Unification of the generating functions for Sheffer type sequences and their applications, preprint", of Sheffer type sequences including the Peters polynomials, the Boole polynomials, the Changhee polynomials, the Simsek polynomials and the Korobov polynomials of the first kind. By making use of these derivative formulas, we provide a recurrence relation and a derivative formula for this unification. Furthermore, by using recurrence relation for this unification, we present miscellaneous special cases of this unification. Finally, we give some derivative formulas related to the well-known Sheffer type sequences such us the Peters polynomials and the Simsek polynomials.