A note on the generalized q-Genocchi measures with weight

Author:

Jolany Hassan,Araci Serkan,Acikgoz Mehmet,Seo Jong-Jin

Abstract

In this paper we investigate special generalized q-Genocchi measures. We introduce q-Genocchi measures with weight alpha. The present paper deals with q-extension of Genocchi measure. Some earlier results of T. Kim in terms of q-Genocchi polynomials can be deduced. We apply the method of generating function, which are exploited to derive further classes of q-Genocchi polynomials and develop q-Genocchi measures. To be more precise, we present the integral representation of p-adic q-Genocchi measure with weight alpha which yields a deeper insight into the effectiveness of this type of generalizations. Generalized q-Genocchi numbers with weight alpha possess a number of interesting properties which we state in this paper.

Publisher

Sociedade Paranaense de Matematica

Subject

General Mathematics

Reference25 articles.

1. 1. Araci, S., Seo, J-J., Erdal, D., New construction weighted (h, q)-Genocchi numbers and polynomials related to zeta type function, Discrete Dynamics in Nature and Society, Volume 2011, Article ID 487490, 7 pages, doi: 10.1155/2011/487490.

2. 2. Araci, S., Erdal, D., Seo, J-J., A study on the fermionic p-adic q-integral representation on Zp Associated with weighted q-Bernstein and q-Genocchi polynomials, Abstract and Applied Analysis(in press).

3. 3. Araci, S., Erdal, D., Kang, D-J., Some New Properties on the q-Genocchi numbers and Polynomials associated with q-Bernstein polynomials, Honam Mathematical J. 33 (2011) no. 2, p. 261-270

4. 4. Araci, S., Aslan, N., Seo, J-J., A Note on the weighted Twisted Dirichlet's type q-Euler numbers and polynomials, Honam Mathematical Journal (in press).

5. 5. Araci, S., Acikgoz, M., Seo, J.J., A study on the weighted q-Genocchi numbers and polynomials with their Interpolation Function, (Submitted)

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