Sums of Involving the Harmonic Numbers and the Binomial Coefficients

DOI: 10.4236/ajcm.2015.52008   PDF   HTML   XML   2,542 Downloads   3,098 Views   Citations

Abstract

Let the numbers be defined by
, where
and are the exponential complete Bell polynomials. In this paper, by means of the methods of Riordan arrays, we establish general identities involving the numbers , binomial coefficients and inverse of binomial coefficients. From these identities, we deduce some identities involving binomial coefficients, Harmonic numbers and the Euler sum identities. Furthermore, we obtain the asymptotic values of some summations associated with the numbers by Darboux’s method.

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Wuyungaowa, &. and Wang, S. (2015) Sums of Involving the Harmonic Numbers and the Binomial Coefficients. American Journal of Computational Mathematics, 5, 96-105. doi: 10.4236/ajcm.2015.52008.

Conflicts of Interest

The authors declare no conflicts of interest.

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