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

Abstract EN

We investigate sums of products of Cauchy numbers including poly-Cauchy numbers: Tm(k)(n)=∑i1+⋯+im=n, i1,…,im≥0(ni1,…,im)ci1⋯cim-1 cim(k) (m≥1,n≥0).

A relation among these sums Tmkn shown in the paper and explicit expressions of sums of two and three products (the case of m=2 and that of m=3 described in the paper) are given.

We also study the other three types of sums of products related to the Cauchy numbers of both kinds and the poly-Cauchy numbers of both kinds.