Analytic properties of the $q$-Volkenborn integral on the ring of $p$-adic integers

Min-Soo Kim; Jin-Woo Son

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2007; 44(1): 1-12

Printed March 1, 2007

Analytic properties of the $q$-Volkenborn integral on the ring of $p$-adic integers

Min-Soo Kim and Jin-Woo Son

Kyungnam University, Kyungnam University

Abstract

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Abstract

In this paper, we consider the $q$-Volkenborn integral of uniformly differentiable functions on the $p$-adic integer ring. By using this integral, we obtain the generating functions of twisted $q$-generalized Bernoulli numbers and polynomials. We find some properties of these numbers and polynomials.

Keywords: $q$-Volkenborn integral, $I_q$-Fourier transforms

MSC numbers: 11E95, 11S80