q-Genocchi Numbers and Polynomials Associated with q-Genocchi-Type l-Functions

Abstract

The main purpose of this paper is to study generating functions of the q-Genocchi numbers and polynomials. We prove a new relation for the generalized q-Genocchi numbers, which is related to the q-Genocchi numbers and q-Bernoulli numbers. By applying Mellin transformation and derivative operator to the generating functions, we define q-Genocchi zeta and l-functions, which are interpolated q-Genocchi numbers and polynomials at negative integers. We also give some applications of the generalized q-Genocchi numbers.