$q$-Volkenborn Integration and Its Applications

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 ${\mathbb{Z}}_p$, 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.

14 pages

References in corpus (1)

• A note on q-Volkenborn integration

Cited by in corpus (3)

• On the Twisted q-Euler numbers and polynomials associated with basic q-l-functions
• A note on the alternating sums of powers of consecutive q-integers
• On p-adic q-l-functions and sums of powers