$q$-Volkenborn Integration and Its Applications

Details $q$-Volkenborn Integration and Its Applications $q$-Volkenborn Integration and Its Applications

2005-10-25

arxiv.org/abs/math/0510524v1

Mathematics

Number Theory

14 pages

Scientific paper

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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