Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2002; 39(2): 221-236

Printed March 1, 2002

Copyright © The Korean Mathematical Society.

Some remarks on a $q$-analogue of Bernoulli numbers

Min-Soo Kim and Jin-Woo Son

Kyungnam University

Abstract

Using the $p$-adic $q$-integral due to T. Kim [4], we define a number $B_n^*(q)$ and a polynomial $B_n^*(x;q)$ which are $p$-adic $q$-analogue of the ordinary Bernoulli number and Bernoulli polynomial, respectively. We investigate some properties of these. Also, we give slightly different construction of Tsumura's $p$-adic function $\ell_{p}(u,s,\chi)$ [14] using the $p$-adic $q$-integral in [4].

Keywords: $q$-analogue, Bernoulli numbers, $p$-adic $q$-integral

MSC numbers: 11B68, 11E95