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arXiv · 1507.04123

Carlitz q-Bernoulli numbers and continued fractions

Frédéric Chapoton·Jiang Zeng
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Abstract

Carlitz has introduced q-analogues of the Bernoulli numbers around 1950. We obtain a representation of these q-Bernoulli numbers (and some shifted version) as moments of some orthogonal polynomials. This also gives factorisations of Hankel determinants of q-Bernoulli numbers, and continued fractions for their generating series. Some of these results are q-analogues of known results for Bernoulli numbers, but some are specific to the q-Bernoulli setting.

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BibTeXRIS

Frédéric Chapoton, Jiang Zeng. 2015-07-15. Carlitz q-Bernoulli numbers and continued fractions. https://arxiv.org/abs/1507.04123

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