A new family of q-analogue of Genocchi numbers and polynomials of higher order

Abstract

In this work, we consider the generating function of Kim's q-Euler polynomials and introduce new generalization of q-Genocchi polynomials and numbers of higher order. Also, we give surprising identities for studying in Analytic Numbers Theory and especially in Mathematical Physics. Moreover, by applying q-Mellin transformation to generating function of q-Genocchi polynomials of higher order and so we define q-Hurwitz-Zeta type function which interpolates of this polynomials at negative integers.