Bernoulli-Carlitz and Cauchy-Carlitz numbers with Stirling-Carlitz numbers
Number Theory
2019-01-07 v2
Abstract
Recently, the Cauchy-Carlitz number was defined as the counterpart of the Bernoulli-Carlitz number. Both numbers can be expressed explicitly in terms of so-called Stirling-Carlitz numbers. In this paper, we study the second analogue of Stirling-Carlitz numbers and give some general formulae, including Bernoulli and Cauchy numbers in formal power series with complex coefficients, and Bernoulli-Carlitz and Cauchy-Carlitz numbers in function fields. We also give some applications of Hasse-Teichm\"uller derivative to hypergeometric Bernoulli and Cauchy numbers in terms of associated Stirling numbers.
Keywords
Cite
@article{arxiv.1704.07135,
title = {Bernoulli-Carlitz and Cauchy-Carlitz numbers with Stirling-Carlitz numbers},
author = {Hajime Kaneko and Takao Komatsu},
journal= {arXiv preprint arXiv:1704.07135},
year = {2019}
}
Comments
This paper has been published in RIMS K\^oky\^uroku Bessatsu B72 (2018),23-35