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Carlitz q-Bernoulli numbers and continued fractions (1507.04123v1)
Published 15 Jul 2015 in math.QA and math.NT
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.