Cauchy–Carlitz numbers

In 1935 Carlitz introduced Bernoulli–Carlitz numbers as analogues of Bernoulli numbers for the rational function field Fr(T)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)Fr(T). Several new identities are also obtained by using Hasse–Teichmüller derivatives.