Novel identities involving Genocchi numbers and polynomials arising from applications of umbral calculus

Abstract

The aim of this paper is to deal with applications of umbral calculus on fermionic p-adic integral on Zp. From those applications, we derive some new identities on Genocchi numbers and polynomials. Moreover, a systemic study of the class of Sheffer sequences on the generating function of Genocchi polynomials are given.