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.
Highlights
Introduction definitions and notationsIn 1, Jang et al gave new formulae on Genocchi numbers
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
Summary
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 give some applications of the generalized q-Genocchi numbers.
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