On sums of consecutive integers
نویسندگان
چکیده
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...
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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