Multivariate Interpolation Functions of Higher-Order-Euler Numbers and Their Applications
Open Access
- 18 March 2008
- journal article
- research article
- Published byย Hindawi Limitedย inย Abstract and Applied Analysis
- Vol.ย 2008, 1-16
- https://doi.org/10.1155/2008/390857
Abstract
The aim of this paper, firstly, is to construct generating functions of ๐-Euler numbers and polynomials of higher order by applying the fermionic ๐-adic ๐-Volkenborn integral, secondly, to define multivariate ๐-Euler zeta function (Barnes-type Hurwitz ๐-Euler zeta function) and ๐-function which interpolate these numbers and polynomials at negative integers, respectively. We give relation between Barnes-type Hurwitz ๐-Euler zeta function and multivariate ๐-Euler ๐-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.Keywords
Funding Information
- Uludag University (F-2006/40, F-2008/31)
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