刘红梅.有关调和数的更多渐近展开公式[J].数学研究及应用,2020,40(3):297~304
有关调和数的更多渐近展开公式
More Asymptotic Expansions for the Harmonic Numbers
投稿时间:2019-05-24  修订日期:2020-03-17
DOI:10.3770/j.issn:2095-2651.2020.03.006
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
基金项目:国家自然科学基金 (Grant No.11501081).
作者单位
刘红梅 大连民族大学理学院, 辽宁 大连 116600 
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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.
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