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Abstract and Applied Analysis
Volume 2008, Article ID 390857, 16 pages
Research Article

Multivariate Interpolation Functions of Higher-Order 𝑞 -Euler Numbers and Their Applications

1Department of Mathematics, Faculty of Arts and Science, University of Uludag, Bursa 16059, Turkey
2Department of Mathematics, Faculty of Arts and Science, University of Akdeniz, Antalya 07058, Turkey

Received 7 December 2007; Accepted 22 January 2008

Academic Editor: Paul Eloe

Copyright © 2008 Hacer Ozden 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.


The aim of this paper, firstly, is to construct generating functions of 𝑞 -Euler numbers and polynomials of higher order by applying the fermionic 𝑝 -adic 𝑞 -Volkenborn integral, secondly, to define multivariate 𝑞 -Euler zeta function (Barnes-type Hurwitz 𝑞 -Euler zeta function) and 𝑙 -function which interpolate these numbers and polynomials at negative integers, respectively. We give relation between Barnes-type Hurwitz 𝑞 -Euler zeta function and multivariate 𝑞 -Euler 𝑙 -function. Moreover, complete sums of products of these numbers and polynomials are found. We give some applications related to these numbers and functions as well.