Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Multivariate Twisted p-Adic q-Integral on Zp Associated with Twisted q-Bernoulli Polynomials and Numbers | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 579509 6 pages doi 2010 579509 Research Article Multivariate Twisted p-Adic q-Integral on Zp Associated with Twisted q-Bernoulli Polynomials and Numbers Seog-Hoon Rim Eun-Jung Moon Sun-Jung Lee and Jeong-Hee Jin Department of Mathematics Kyungpook National University Daegu 702-701 Republic of Korea Correspondence should be addressed to Seog-Hoon Rim shrim@ Received 19 June 2010 Accepted 2 October 2010 Academic Editor Ulrich Abel Copyright 2010 Seog-Hoon Rim et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Recently many authors have studied twisted q-Bernoulli polynomials by using the p-adic invariant q-integral on Zp. In this paper we define the twisted p-adic q-integral on Zp and extend our result to the twisted q-Bernoulli polynomials and numbers. Finally we derive some various identities related to the twisted q-Bernoulli polynomials. 1. Introduction Let p be a fixed prime number. Throughout this paper the symbols Z Zp Qp C and Cp will denote the ring of rational integers the ring of p-adic integers the field of p-adic rational numbers the complex number field and the completion of the algebraic closure of Qp respectively. Let N be the set of natural numbers and Z N u 0 . Let vp be the normalized exponential valuation of Cp with p p p V p 1 p. When one talks of q-extension q is variously considered as an indeterminate a complex q e C or p-adic number q e Cp. If q e C one normally assumes that q 1. If q e Cp then we assume that q - 1 p 1. For n e N let Tp be the p-adic locally constant space defined by Tp u Cpn lim Cpn Cp n 1 n where Cpn Z e Cp zpn 1 for some n 0 is the cyclic group of order pn. 2 Journal of Inequalities and Applications Let UD Zp be the space of uniformly .
