TITLE:
Sums of Involving the Harmonic Numbers and the Binomial Coefficients
AUTHORS:
Wuyungaowa, Sudan Wang
KEYWORDS:
Harmonic Numbers, Euler Sum, Riordan Arrays, Asymptotic Values
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.5 No.2,
May
25,
2015
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.