منابع مشابه
Sums of Consecutive Integers
Wai Yan Pong ([email protected]) received his B.Sc. from the Chinese University of Hong Kong and his M.Sc. and Ph.D. from the University of Illinois at Chicago. He was a Doob Research Assistant Professor at the University of Illinois at Urbana-Champaign for three years. He then moved to California and is now teaching at California State University, Dominguez Hills. His research interests are in m...
متن کاملOn the alternating sums of powers of consecutive q-integers
In this paper we construct q-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the q-analogue of alternating sums of powers of consecutive integers due to Euler. 2000 Mathematics Subject Classification : 11S80, 11B68
متن کاملq-ANALOGUES OF THE SUMS OF POWERS OF CONSECUTIVE INTEGERS
Let n, k be the positive integers (k > 1), and let Sn,q(k) be the sums of the n-th powers of positive q-integers up to k − 1: Sn,q(k) = ∑k−1 l=0 ql. Following an idea due to J. Bernoulli, we explore a formula for Sn,q(k).
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In this paper we construct the q-analogue of Barnes's Bernoulli numbers and polynomials of degree 2, for positive even integers, which is an answer to a part of Schlosser's question. For positive odd integers, Schlosser's question is still open. Finally, we will treat the q-analogue of the sums of powers of consecutive integers.
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ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 2005
ISSN: 0033-569X,1552-4485
DOI: 10.1090/s0033-569x-05-00991-1