| 关于正整数幂的多重卷积公式 |
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| 引用本文： | 林杨,郑德印.关于正整数幂的多重卷积公式[J].杭州师范学院学报(自然科学版),2009,8(5):327-330,349. |
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| 作者姓名： | 林杨 郑德印 |
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| 作者单位： | 杭州师范大学理学院,浙江杭州,310036 |
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| 基金项目： | 浙江省自然科学基金项目 |
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| 摘 要： | 若k个正整数的和为n,那么这k个正整数积的r次幂的多重和就是正整数的r次幂的k重卷积.使用生成函数方法首先得到了一次幂和二次幂的k重卷积的求和公式,然后借助于导数算子和第二类Stirling数给出了一般的r次幂的k重卷积的求和公式.
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| 关 键 词： | 多重卷积 生成函数 第二类Stirling数 |
Multiple Convolution Formulas on Powers of Positive Integers |
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| LIN Yang,ZHENG De-yin.Multiple Convolution Formulas on Powers of Positive Integers[J].Journal of Hangzhou Teachers College(Natural Science),2009,8(5):327-330,349. |
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| Authors: | LIN Yang ZHENG De-yin |
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| Institution: | (College of Science, Hangzhou Normal University, Hangzhou 310036, China) |
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| Abstract: | If a sum of k positive integers equals to n, the multiple sum of the r-th powers of the product of these k positive integers is a k-fold convolution of the r-th powers of the positive integers. By means of generating function method, summation formulas of the k fold convolution of simple and double power are derived. Furthermore, the k-fold convolution formulas on the general r-th powers of positive integers are established with the derivative operator and the Stirling numbers of the second kind. |
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| Keywords: | multiple convolution generating function Stirling number of the second kind |
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