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 Remarks on Sum of Products of h, q -Twisted Euler Polynomials and Numbers | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 816129 8 pages doi 2008 816129 Research Article Remarks on Sum of Products of h q -Twisted Euler Polynomials and Numbers Hacer Ozden 1 Ismail Naci Cangul 1 and Yilmaz Simsek2 1 Department of Mathematics Faculty of Arts and Science University ofUludag 16059 Bursa Turkey 2 Department of Mathematics Faculty of Arts and Science University ofAkdeniz 07058 Antalya Turkey Correspondence should be addressed to Hacer Ozden hozden@ Received 29 March 2007 Accepted 16 October 2007 Recommended by Panayiotis D. Siafarikas The main purpose of this paper is to construct generating functions of higher-order twisted h q -extension of Euler polynomials and numbers by using p-adic q-deformed fermionic integral on Zp. By applying these generating functions we prove complete sums of products of the twisted h q -extension of Euler polynomials and numbers. We also define some identities involving twisted h q -extension of Euler polynomials and numbers. Copyright 2008 Hacer Ozden 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 definitions and notations Higher-order twisted Bernoulli and Euler numbers and polynomials were studied by many authors see for details 1-10 . In 1 3 Kim constructed p-adic q-Volkenborn integral identities. He proved p-adic q-integral representation of q-Euler and Bernoulli numbers and polynomials. In 11 the second author constructed a new approach to the complete sums of products of h q -extension of higher-order Euler polynomials and numbers. Kim and Rim 12 by using q-deformed fermionic integral on Zp defined twisted generating functions of the q-Euler numbers and polynomials respectively. By using these functions they also constructed interpolation functions of these
