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 Sums of Products of q-Euler Polynomials and Numbers | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 381324 8 pages doi 2009 381324 Research Article Sums of Products of q-Euler Polynomials and Numbers Young-Hee Kim 1 Kyung-Won Hwang 2 and Taekyun Kim1 1 Division of General Education-Mathematics Kwangwoon University Seoul 139-701 South Korea 2 Department of General education Kookmin University Seoul 136-702 South Korea Correspondence should be addressed to Kyung-Won Hwang khwang7@ Received 4 March 2009 Accepted 25 April 2009 Recommended by Vijay Gupta We derive formulae for the sums of products of the q-Euler polynomials and numbers using the multivariate fermionic p-adic q-Volkenborn integral on Zp. Copyright 2009 Young-Hee Kim 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. 1. Introduction The purpose of this paper is to derive formulae for the sums of products of the q-Euler polynomials and numbers since many identities can be obtained from our sums of products of the q-Euler polynomials and numbers. In 1 Simsek evaluated the complete sums for the Euler numbers and polynomials and obtained some identities related to Euler numbers and polynomials from his complete sums and Jang et al. 2 also considered the sums of products of Euler numbers. Kim 3 derived the sums of products of the q-Euler numbers using the fermionic p-adic q-Volkenborn integral. In this paper we will evaluate the complete sum of the q-Euler polynomials and numbers using the fermionic p-adic q-Volkenborn integral on Zp. Assume that p is a fixed odd prime. Throughout this paper the symbols Zp Qp C and Cp denote the ring of p-adic rational integers the field of p-adic rational numbers the complex number field and the completion of algebraic closure of Qp respectively. Let N be the set of natural numbers. Let Vp be the
