Multivariate Interpolation Functions of Higher‐Order <i>q</i>‐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.