Title: Bernoulli-Carlitz and Cauchy-Carlitz numbers with Stirling-Carlitz numbers,
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.