A note on the modified q-Genocchi numbers and polynomials with weight (\alpha,\beta) and their interpolation function at negative integers
Abstract
The purpose of this paper concerns to establish modified q-Genocchi numbers and polynomials with weight ({\alpha},{\beta}). In this paper we investigate special generalized q-Genocchi polynomials and we apply the method of generating function, which are exploited to derive further classes of q-Genocchi polynomials and develop q-Genocchi numbers and polynomials. By using the Laplace-Mellin transformation integral, we define q-Zeta function with weight ({\alpha},{\beta}) and by presenting a link between q-Zeta function with weight ({\alpha},{\beta}) and q-Genocchi numbers with weight ({\alpha},{\beta}) we obtain an interpolation formula for the q-Genocchi numbers and polynomials with weight ({\alpha},{\beta}). Also we derive distribution formula (Multiplication Theorem) and Witt's type formula for modified q-Genocchi numbers and polynomials with weight ({\alpha},{\beta}) which yield a deeper insight into the effectiveness of this type of generalizations for q=Genocchi numbers and polynomials. Our new generating function possess a number of interesting properties which we state in this paper.
Keywords
Cite
@article{arxiv.1112.5902,
title = {A note on the modified q-Genocchi numbers and polynomials with weight (\alpha,\beta) and their interpolation function at negative integers},
author = {Serkan Araci and Mehmet Açikgöz and Feng Qi and Hassan Jolany},
journal= {arXiv preprint arXiv:1112.5902},
year = {2014}
}
Comments
9 pages, submitted