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Publication Date:
25 11 2009
DOI:
10.1515/INTEG.2009.048

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Integers

Editor-in-Chief: Nathanson, Melvyn B. / Nešetril, Jaroslav / Pomerance, Carl

6 Issues per year

Mathematical Citation Quotient 2010: 0.20

Some Results for Generalized Harmonic Numbers

Feng, Cong-Jiao 1 / Zhao, Feng-Zhen 2

1School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China. E-mail:

2School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China. E-mail:

Citation Information: Integers. Volume 9, Issue 5, Pages 605–619, ISSN (Print) 1867-0652, DOI: 10.1515/INTEG.2009.048, November 2009

Publication History:

Received: 08/07/2007;
Revised: 13/06/2009;
Accepted: 04/08/2009;
Published Online: 05/03/2012

Abstract

In this paper, we discuss the properties of a class of generalized harmonic numbers H(n, r). By means of the method of coefficients, we establish some identities involving H(n, r). We obtain a pair of inversion formulas. Furthermore, we investigate certain sums related to H(n, r), and give their asymptotic expansions. In particular, we obtain the asymptotic expansion of certain sums involving H(n, r) and the inverse of binomial coefficients by Laplace's method.

Keywords.: Harmonic numbers; Cauchy numbers; associated Stirling numbers; asymptotic expansion

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