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 On the Distribution of the q-Euler Polynomials and the q-Genocchi Polynomials of Higher Order | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 723615 9 pages doi 2008 723615 Research Article On the Distribution of the q-Euler Polynomials and the q-Genocchi Polynomials of Higher Order Leechae Jang1 and Taekyun Kim2 1 Department of Mathematics and Computer Science KonKuk University Chungju 380-701 South Korea 2 Division of General Education-Mathematics Kwangwoon University Seoul 139-701 South Korea Correspondence should be addressed to Leechae Jang Received 19 March 2008 Accepted 23 October 2008 Recommended by Laszlo Losonczi In 2007 and 2008 Kim constructed the q-extension of Euler and Genocchi polynomials of higher order and Choi-Anderson-Srivastava have studied the q-extension of Euler and Genocchi numbers of higher order which is defined by Kim. The purpose of this paper is to give the distribution of extended higher-order q-Euler and q-Genocchi polynomials. Copyright 2008 L. Jang and T. Kim. 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 Euler numbers En and polynomials En x are defined by the generating function in the complex number field as 2 o tn . 7i gEnni 0 1 n 0 1-1 2 o n -T exi ZFn x n I I n e n 0 n cf. 1-4 . The Bernoulli numbers Bn and polynomials Bn x are defined by the generating function as o n e -1 nn rt o n er-1ex - gB x n 2 Journal of Inequalities and Applications cf. 5-8 . The Genocchi numbers Gn and polynomials Gn x are defined by the generating function as 2t el 1 z Gntn 0 n -2-ext z Gn tn et 1 nz0 n cf. 9 10 . It satisfies G0 0 G1 1 . and for n 1 _ 1 Gn 2n Bn 2 - Bn . Let p be a fixed odd prime number. Throughout this paper Zp Qp and Cp will be respectively the ring of p-adic rational integers the field of p-adic rational numbers and the p-adic completion of the .
