Cauchy-Carlitz numbers

preprint2015arXivOpen access

In 1935 Carlitz introduced Bernoulli-Carlitz numbers as analogues of Bernoulli numbers for the rational function field $\mathbb F_r(T)$ . In this paper, we introduce Cauchy-Carlitz numbers as analogues of Cauchy numbers. By using Stirling-Carlitz numbers, we give their arithmetical and combinatorial properties and relations with Bernoulli-Carlitz numbers for $\mathbb F_r(T)$ . Several new identities are also obtained by using Hasse-Teichimüller derivatives.

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Cauchy-Carlitz numbers

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