| 用高阶导数对自然数方幂和相关问题的研究 |
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| 引用本文： | 赵新华,代国伟. 用高阶导数对自然数方幂和相关问题的研究[J]. 云南民族大学学报(自然科学版), 2010, 19(6). DOI: 10.3969/j.issn.1672-8513.2010.06.017 |
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| 作者姓名： | 赵新华 代国伟 |
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| 作者单位： | 1. 中国农业银行三门峡分行,河南,三门峡,472000
2. 西北师范大学,数学与信息科学学院,甘肃,兰州,730070 |
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| 摘 要： | 利用ekx和(ex-1)k的高阶导数的性质,简捷地推导出了自然数方幂和的2种形式的求和公式,得到了2个Bernoulli数的确切公式.所得到的结果推广了传统自然数方幂和的相关结论.
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| 关 键 词： | 自然数的方幂和 高阶导数 第2类Stirling数 Bernoulli数 莱布尼茨公式 |
Study on the Power Sum of Natural Numbers with Higher Order Derivative |
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| ZHAO Xin-hua,DAI Guo-wei. Study on the Power Sum of Natural Numbers with Higher Order Derivative[J]. Journal of Yunnan Nationalities University:Natural Sciences Edition, 2010, 19(6). DOI: 10.3969/j.issn.1672-8513.2010.06.017 |
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| Authors: | ZHAO Xin-hua DAI Guo-wei |
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| Affiliation: | ZHAO Xin-hua1,DAI Guo-wei2(1.Sanmenxia Branch,Agricultural Bank of China,Sanmenxia 472000,China,2.College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China) |
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| Abstract: | Using the properties of the higher order derivative of ekx and(ex-1)k,two summation formulas for the power sum of natural numbers were established and two explicit formulas for Bemoulli numbers were obtained,which is a generalization of the traditional power sum of natural numbers. |
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| Keywords: | power sum of natural numbers higher order derivative Stirling numbers of the second kind Bernoulli number Leibniz's formula |
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