Carlitz q-Bernoulli numbers and continued fractions
Quantum Algebra
2015-07-16 v1 Number Theory
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.
Keywords
Cite
@article{arxiv.1507.04123,
title = {Carlitz q-Bernoulli numbers and continued fractions},
author = {Frédéric Chapoton and Jiang Zeng},
journal= {arXiv preprint arXiv:1507.04123},
year = {2015}
}
Comments
16 pages, in French, no figure