Note on the sums of powers of consecutive $q$-integers

Details Note on the sums of powers of consecutive $q$-integers Note on the sums of powers of consecutive $q$-integers

2005-03-11

arxiv.org/abs/math/0503209v1

Mathematics

Number Theory

10 pages

Scientific paper

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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