| 有关调和数的更多渐近展开公式 |
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| 引用本文： | 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. |
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| 作者姓名： | 刘红梅 |
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| 作者单位： | 大连民族大学理学院, 辽宁 大连 116600 |
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| 基金项目： | 国家自然科学基金 (Grant No.11501081). |
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| 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,
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| 关 键 词： | 渐近展开 调和数 Bell多项式 |
| 收稿时间： | 2019/5/24 0:00:00 |
| 修稿时间： | 2020/3/17 0:00:00 |
More Asymptotic Expansions for the Harmonic Numbers |
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| Hongmei LIU.More Asymptotic Expansions for the Harmonic Numbers[J].Journal of Mathematical Research with Applications,2020,40(3):297-304. |
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| Authors: | Hongmei LIU |
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| Institution: | School of Science, Dalian Minzu University, Liaoning 116600, P. R. China |
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| Abstract: | 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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| Keywords: | asymptotic expansions harmonic numbers Bell polynomials |
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