Sums of Involving the Harmonic Numbers and the Binomial Coefficients

• 作者: Wuyungaowa Sudan Wang
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: HARMONIC Numbers EULER SUM Riordan ARRAYS ASYMPTOTIC Values
• 年，卷（期）: 2015,（2）
• 页码范围: 96-105
• 页数: 10页
• 分类号: O1

摘要

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.