Multivariate Interpolation Functions of Higher-Order $q$-Euler Numbers and Their Applications
Hacer Ozden, Ismail Naci Cangul, and Yilmaz Simsek
Source: Abstr. Appl. Anal. Volume 2008
(2008), Article ID
390857, 16 pages.
Abstract
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.
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Permanent link to this document: http://projecteuclid.org/euclid.aaa/1220969153
Digital Object Identifier: doi:10.1155/2008/390857
Mathematical Reviews number (MathSciNet): MR2393118
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Abstract and Applied Analysis
