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 Multiple Twisted q-Euler Numbers and Polynomials Associated with p-Adic q-Integrals | Hindawi Publishing Corporation Advances in Difference Equations Volume 2008 Article ID 738603 11 pages doi 2008 738603 Research Article Multiple Twisted q-Euler Numbers and Polynomials Associated with p-Adic q-Integrals Lee-Chae Jang Department of Mathematics and Computer Science Konkuk University Chungju 380701 South Korea Correspondence should be addressed to Lee-Chae Jang Received 14 January 2008 Revised 25 February 2008 Accepted 26 February 2008 Recommended by Martin Bohner By using p-adic q-integrals on Zp we define multiple twisted q-Euler numbers and polynomials. We also find Witt s type formula for multiple twisted q-Euler numbers and discuss some characterizations of multiple twisted q-Euler Zeta functions. In particular we construct multiple twisted Barnes type q-Euler polynomials and multiple twisted Barnes type q-Euler Zeta functions. Finally we define multiple twisted Dirichlet s type q-Euler numbers and polynomials and give Witt s type formula for them. Copyright 2008 Lee-Chae Jang. 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. 1. Introduction Let p be a fixed odd prime number. Throughout this paper Zp Qp and Cp are respectively the ring of p-adic rational integers the field of p-adic rational numbers and the p-adic completion of the algebraic closure of Qp. The p-adic absolute value in Cp is normalized so that p p 1 p. When one talks about q-extension q is variously considered as an indeterminate a complex number q G C or a p-adic number q G Cp. If q G C one normally assumes that q 1. If q G Cp one normally assumes that 1 - q p p 1 p h so that qx exp x log q for each x G Zp. We use the notations x q 1 - qx T-Ĩ x -q 1 - Hr 1 q cf. 1-14 for all x G Zp. For a fixed odd positive integer d with p d 1 set X Xd lim Z dpnZ X1 Zp n 2 Advances in Difference .
