Generalization of Mellin derivative and its applications

Abstract

In this paper we define generalized exponential polynomials by means of the generalization of the Mellin derivative (xD). We give different proofs for some known results and obtain a new recurrence relation and a new operator formula for generalized exponential polynomials. We also define generalized geometric polynomials by means of the generalization of the Mellin derivative (xD) and obtain their basic properties.