Sums of Products of Cauchy Numbers, Including Poly-Cauchy Numbers. (30th January 2013) - Komatsu, Takao
Abstract : We investigate sums of products of Cauchy numbers including poly-Cauchy numbers: T m ( k ) ( n ) = ∑ i 1 + ⋯ + i m = n, i 1, …, i m ≥ 0 ( n i 1, …, i m ) c i 1 ⋯ c i m - 1 c i m ( k ) ( m ≥ 1, n ≥ 0 ) . A relation among these sums T m k n 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.