Sums of Products of Cauchy Numbers, Including Generalized Poly-Cauchy Numbers

Abstract

Many researchers have investigated sums of products of Bernoulli numbers and related types of sums of products. Recently, the concept of poly-Cauchy numbers has been introduced by the author as a generalization of the classical Cauchy number. In this paper, we investigate sums of products of Cauchy numbers including generalized poly-Cauchy numbers. We give a relation among these sums and explicit expressions of sums of any arbitrary products. In addition, we also show the similar results in the case of poly-Cauchy numbers of the second kind and those of mixed ones of both kinds.