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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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\textit{H. Özden} et al., Abstr. Appl. Anal. 2008, Article ID 390857, 16 p. (2008; Zbl 1140.11313)

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