Bernoulli-Carlitz and Cauchy-Carlitz numbers with Stirling-Carlitz numbers
arXiv:1704.07135
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-Teichmüller derivative to hypergeometric Bernoulli and Cauchy numbers in terms of associated Stirling numbers.
arXiv commentThis paper has been published in RIMS Kôkyûroku Bessatsu B72 (2018),23-35