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$q$-Volkenborn Integration and Its Applications

Taekyun Kim
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Abstract

The main purpose of this paper is to present a systemic study of some families of multiple $q$-Euler numbers and polynomials. In particular, by using the $q$-Volkenborn integration on $\Bbb Z_p$, we construct $p$-adic $q$-Euler numbers and polynomials of higher order. We also define new generating functions of multiple $q$-Euler numbers and polynomials. Furthermore, we construct Euler $q$-Zeta function. This paper is the version of the preprint of my paper to publish in the special issues as the preprint part of this proceedings.

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Taekyun Kim. 2005-10-25. $q$-Volkenborn Integration and Its Applications. https://arxiv.org/abs/math/0510524

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