<inline-formula> <graphic file="1687-1847-2008-815750-i1.gif"/></inline-formula>-Genocchi Numbers and Polynomials Associated with <inline-formula> <graphic file="1687-1847-2008-815750-i2.gif"/></inline-formula>-Genocchi-Type <inline-formula> <graphic file="1687-1847-2008-815750-i3.gif"/></inline-formula>-Functions

Abstract

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