Abstract
In this paper, we introduce the Bernoulli polynomials with the variable [x]q and we get polynomials related to the Bernoulli polynomials with the variable [x]q and the Bernoulli numbers as coecients. This Bernoulli polynomials is dened by the p-adic integral and we get the some interesting properties. Also we study the analogue zeta function using the Bernoulli polynomials with the variable [x]q. Mathematics Subject Classication: 11B68, 11S40, 11S80
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