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Multivariate interpolation functions of higher-order \(q\)-Euler numbers and their applications. (English) Zbl 1140.11313

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.

MSC:

11B68 Bernoulli and Euler numbers and polynomials
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
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References:

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