与正整数的k次幂补数有关的恒等式
Identities on the k-th Power Complements
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摘要: 设m≥2是一个给定的正整数,n是任意自然数,am(n)表示n的m次幂补数。利用初等方法研究了级数\sum\limits_n = 1^\infty \fracn\left(na_m\left(n \right) \right)^s (其中s是实部大于等于2的任一复数)的均值性质,得到3个恒等式。Abstract: For any given positive integer m≥2 and any natural number n, we call am(n) represents a m-th power complement number. Elementary methods is used to study the mean value properties of the series \sum\limits_n = 1^\infty \fracn\left(na_m\left(n \right) \right)^s , where s is a complex number with Res≥2, and several identities are work out.