Analytic properties of the $q$-Volkenborn integral on the ring of $p$-adic integers
Bull. Korean Math. Soc. 2007 Vol. 44, No. 1, 1-12
Printed March 1, 2007
Min-Soo Kim and Jin-Woo Son
Kyungnam University, Kyungnam University
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
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