Cauchy-Carlitz numbers
Abstract
In 1935 Carlitz introduced Bernoulli-Carlitz numbers as analogues of Bernoulli numbers for the rational function field Fr(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 Fr(T). Several new identities are also obtained by using Hasse-Teichim\"uller derivatives.
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