复级数列N次方倒数和的收敛性与部分复级数求和

The Convergence Properties and the Sum of Inverse N Times Square of Complex Series

求解自然数平方倒数和这个无穷级数的和是历史上有名的难题,欧拉创造性的应用函数的级数展开式与多项式根与系数的关系的类比方法解决了这个难题,后来这个人们发现这个问题也可以利用傅里叶来求解,本文通过对历史上这类倒数N次方求和问题的解答得出来在复平面上复数列N次方倒数收敛性的判断条件与部分级数的求解。

To solve the inverse square natural numbers and the sum of infinite series is a history famous problem, Euler creatively use the method of analogy between series expansion and the root of the polynomial with coefficients to solve this problem, then people found this problem can also besolved by Fourier series expansion,.According to solve this kind of reciprocal n times party history and problems of work it out for n square reciprocal convergence judgment condition and part series on the complex plane complex series.