Some Properties of a New Class of Generalized Cauchy Numbers

Feng-Zhen Zhao1
1Department of Mathematics, Shanghai University, Shanghai 200444, China.

Abstract

In this paper, we investigate properties of a new class of generalized Cauchy numbers. By using the method of coecient, we establish a series of identities involving generalized Cauchy numbers, which generalize some results for the Cauchy numbers. Furthermore, we give some asymptotic approximations of certain sums related to the generalized Cauchy numbers.

Keywords: Cauchy numbers, harmonic numbers, Stirling numbers, asymptotic approximation.