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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2007; 44(2): 487-498

Printed March 1, 2007

Copyright © The Korean Mathematical Society.

Generalized harmonic number identities and a related matrix representation

Gi-Sang Cheon and Moawwad E. A. El-Mikkawy

Sungkyunkwan University, Mansoura University

Abstract

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In this paper, we obtain important combinatorial identities of generalized harmonic numbers using symmetric polynomials. We also obtain the matrix representation for the generalized harmonic numbers whose inverse matrix can be computed recursively.

Keywords: harmonic numbers, Riemann zeta function, Stirling numbers, Bernoulli numbers, symmetric polynomials

MSC numbers: 05A30

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