tailieunhanh - Báo cáo hóa học: " q-Bernoulli numbers and q-Bernoulli polynomials revisited"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : q-Bernoulli numbers and q-Bernoulli polynomials revisited | Ryoo et al. Advances in Difference Equations 2011 2011 33 http content 2011 1 33 RESEARCH o Advances in Difference Equations a SpringerOpen Journal Open Access q-Bernoulli numbers and q-Bernoulli polynomials revisited Cheon Seoung Ryoo1 Taekyun Kim2 and Byungje Lee3 Correspondence ryoocs@ department of Mathematics Hannam University Daejeon 306791 Korea Full list of author information is available at the end of the article Abstract This paper performs a further investigation on the q-Bernoulli numbers and q-Bernoulli polynomials given by Acikgoz et al. Adv Differ Equ Article ID 951764 9 2010 some incorrect properties are revised. It is point out that the generating function for the q-Bernoulli numbers and polynomials is unreasonable. By using the theorem of Kim Kyushu J Math 48 73-86 1994 see Equation 9 some new generating functions for the q-Bernoulli numbers and polynomials are shown. Mathematics Subject Classification 2000 11B68 11S40 11S80 Keywords Bernoulli numbers and polynomials q-Bernoulli numbers and polynomials q-Bernoulli numbers and polynomials 1. Introduction As well-known definition the Bernoulli polynomials are given by ex eB x t Bn x ttn e 1 n n 0 see 1-4 with usual convention about replacing Bn x by Bn x . In the special case x 0 Bn 0 Bn are called the nth Bernoulli numbers. Let us assume that q e c with q 1 as an indeterminate. The q-number is defined by lxf 1 q 1 q see 1-6 . Note that limq 1 x q x. Since Carlitz brought out the concept of the q-extension of Bernoulli numbers and polynomials many mathematicians have studied q-Bernoulli numbers and q-Bernoulli polynomials see 1 7 5 6 8-12 . Recently Acikgoz Erdal and Araci have studied to a new approach to q-Bernoulli numbers and q-Bernoulli polynomials related to q-Bern-stein polynomials see 7 . But their generating function is unreasonable. The wrong properties are indicated by some counter-examples and they are corrected. It is point out that Acikgoz .

TÀI LIỆU LIÊN QUAN
crossorigin="anonymous">
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.