On Cauchy Numbers and Their Generalizations

Abstract

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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