Sums of Products of Cauchy Numbers, Including Poly-Cauchy Numbers. (30th January 2013)

• Record Type: Journal Article
• Authors: Komatsu, Takao
• Other Names: Cheon Gi Sang Academic Editor.
• Is Part Of: Journal of discrete mathematics. Volume 2013(2013)
• Publication Date: 2013-01-30
• Subjects: Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.1155/2013/373927
• Languages: English
• ISSNs: 2090-9837

Abstract

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.