有关调和数的更多渐近展开公式

More Asymptotic Expansions for the Harmonic Numbers

中文关键词:  渐近展开  调和数  Bell多项式

英文关键词:asymptotic expansions  harmonic numbers  Bell polynomials

中文摘要:

      基于指数型完全Bell多项式,建立了一个一般调和数渐近展开式,并给出展开式中系数的相应递推关系.由生成函数方法进一步推导出这些系数的具体表达式.另外,我们建立了两个在对数项里只含有奇数或偶数次幂项的lacunary调和数渐近展开式,

英文摘要:

      In this paper, by exponential complete Bell polynomials, we establish a (general) harmonic number asymptotic expansion, and give the corresponding recurrence of the coefficient sequence in the expansion. By the methods of the generating functions and summation transformations, we also present an explicit expression for the coefficient sequence of the expansion. Moreover, we establish two (general) lacunary harmonic number asymptotic expansions, which contain only even or odd power terms in the logarithmic term.