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Using the p-adic q-integral due to T. Kim , 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 p (u, s, χ)  using the p-adic q-integral in  .doi:10.4134/jkms.2002.39.2.221 fatcat:6yudbmhdjfa3fnlclco33h4wwe