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

Y. Simsek·D. Kim·T. Kim·S. H. Rim
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Abstract

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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Y. Simsek, D. Kim, T. Kim, S. H. Rim. 2005-03-11. Note on the sums of powers of consecutive $q$-integers. https://arxiv.org/abs/math/0503209

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