tailieunhanh - Báo cáo hóa học: " Research Article Congruences for Generalized q-Bernoulli Polynomials"

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 Congruences for Generalized q-Bernoulli Polynomials | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 270713 19 pages doi 2008 270713 Research Article Congruences for Generalized -Bernoulli Polynomials Mehmet Cenkci and Veli Kurt Department of Mathematics Akdeniz University 07058 Antalya Turkey Correspondence should be addressed to Mehmet Cenkci cenkci@ Received 9 December 2007 Accepted 15 February 2008 Recommended by Andrea Laforgia In this paper we give some further properties of p-adic q-L-function of two variables which is recently constructed by Kim 2005 and Cenkci 2006 . One of the applications of these properties yields general classes of congruences for generalized q-Bernoulli polynomials which are q-extensions of the classes for generalized Bernoulli numbers and polynomials given by Fox 2000 Gunaratne 1995 and Young 1999 2001 . Copyright 2008 M. Cenkci and V. Kurt. 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 and primary concepts For n G Z n 0 Bernoulli numbers Bn originally arise in the study of finite sums of a given power of consecutive integers. They are given by B0 1 B1 -1 2 B2 1 6 B3 0 B4 -1 30 . with B2n 1 0 for odd n 1 and Bn -- n n Bm n 1 m m 0 for all n 1. In the symbolic notation Bernoulli numbers are given recursively by B 1 n - Bn - ổn with the usual convention about replacing Bj by Bj where ổn 1 is the Kronecker symbol. The Bernoulli polynomials Bn z can be expressed in the form n Bn z B zr 2 m 0 2 Journal of Inequalities and Applications for an indeterminate z. The generating functions of these numbers and polynomials are given respectively by Ft tA ẳ B -e -1 0 n t . t tn F z e-ĩ e j B- n for t 2 n. One of the notable facts about Bernoulli numbers and polynomials is the relation between the Riemann and the Hurwitz or generalized .