Multivariate interpolation functions of higher-order \(q\)-Euler numbers and their applications (Q938360)

Summary: 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.