## Abstract and Applied Analysis

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

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 390857, 16 pages.

Dates
First available in Project Euclid: 9 September 2008

https://projecteuclid.org/euclid.aaa/1220969153

Digital Object Identifier
doi:10.1155/2008/390857

Mathematical Reviews number (MathSciNet)
MR2393118

Zentralblatt MATH identifier
1140.11313

#### Citation

Ozden, Hacer; Cangul, Ismail Naci; Simsek, Yilmaz. Multivariate Interpolation Functions of Higher-Order $q$ -Euler Numbers and Their Applications. Abstr. Appl. Anal. 2008 (2008), Article ID 390857, 16 pages. doi:10.1155/2008/390857. https://projecteuclid.org/euclid.aaa/1220969153

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