THEOREMS ON GENOCCHI POLYNOMIALS OF HIGHER ORDER ARISING FROM GENOCCHI BASIS

-Genocchi Polynomials and Numbers of Higher Order

Copyright q 2010 Lee-Chae Jang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We investigate several arithmetic properties of h, q-Genocchi polynomials and numbers of higher order.

On Genocchi Numbers and Polynomials

Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, C, and Cp will, respectively, denote the ring of p-adic rational integers, the field of p-adic rationalnumbers, the complex number field, and the completion of the algebraic closure of Qp. Let vp be the normalized exponential valuation of Cp with |p|p p−vp p 1/p. When one talks about q-extension, q is variously considered as an i...

On the Generalized q-Genocchi Numbers and Polynomials of Higher-Order

where we use the technical method’s notation by replacing G x by Gn x , symbolically, see 1, 2 . In the special case x 0, Gn Gn 0 are called the nth Genocchi numbers. From the definition of Genocchi numbers, we note that G1 1, G3 G5 G7 · · · 0, and even coefficients are given by G2n 2 1 − 22n B2n 2nE2n−1 0 see 3 , where Bn is a Bernoulli number and En x is an Euler polynomial. The first few Gen...

Integral Formulae of Bernoulli and Genocchi Polynomials

On the Hurwitz-type q-Genocchi Zeta Functions and q-Genocchi Polynomials

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In [2], we introduced the q-Genocchi numbers and polynomials with weak weight α. In this paper, we investigate some properties which are related to q-Genocchi numbers G (α) n,q and polynomials G (α) n,q (x) with weak weight α.