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arXiv · 1704.07135

Bernoulli-Carlitz and Cauchy-Carlitz numbers with Stirling-Carlitz numbers

Hajime Kaneko·Takao Komatsu
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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.

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Hajime Kaneko, Takao Komatsu. 2017-04-24. Bernoulli-Carlitz and Cauchy-Carlitz numbers with Stirling-Carlitz numbers. https://arxiv.org/abs/1704.07135

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