Journal of Integer Sequences, Vol. 15 (2012), Article 12.9.6

Identities Involving Generalized Harmonic Numbers and Other Special Combinatorial Sequences

Huyile Liang and Wuyungaowa
Department of Mathematics
College of Sciences and Technology
Inner Mongolia University
Hohhot 010021
P. R. China


In this paper, we study the properties of the generalized harmonic numbers Hn,k,r(α,β). In particular, by means of the method of coefficients, generating functions and Riordan arrays, we establish some identities involving the numbers Hn,k,r(α,β), Cauchy numbers, generalized Stirling numbers, Genocchi numbers and higher order Bernoulli numbers. Furthermore, we obtain the asymptotic values of some summations associ- ated with the numbers Hn,k,r(α,β) by Darboux's method and Laplace's method.

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Received October 25 2012; revised version received November 20 2012. Published in Journal of Integer Sequences, December 27 2012.

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