Multivariate Interpolation Functions of Higher-Orderq-Euler Numbers and Their Applications

Abstract
The aim of this paper, firstly, is to construct generating functions of ๐‘ž-Euler numbers and polynomials of higher order by applying the fermionic ๐‘-adic ๐‘ž-Volkenborn integral, secondly, to define multivariate ๐‘ž-Euler zeta function (Barnes-type Hurwitz ๐‘ž-Euler zeta function) and ๐‘™-function which interpolate these numbers and polynomials at negative integers, respectively. We give relation between Barnes-type Hurwitz ๐‘ž-Euler zeta function and multivariate ๐‘ž-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.
Funding Information
  • Uludag University (F-2006/40, F-2008/31)

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