Levent KARGIN

On Cauchy Numbers and Their Generalizations

This paper is concerned with both kinds of the Cauchy numbers and their generalizations. Taking into account Mellin derivative, we relate p-Cauchy numbers of the second kind with shifted Cauchy numbers of the first kind, which yields new explicit formulas for the Cauchy numbers of the both kind. We introduce a generalization of the Cauchy numbers and investigate several properties, including recurrence relations, convolution identities and generating functions. In particular, these results give rise to new identities for Cauchy numbers.

Keywords:

Cauchy numbers, Poly-Cauchy numbers, p-Cauchy numbers, Generating function Recurrence relations,

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