一个无穷级数的和

Sum of One Infinite Series

由[1,2 826]知,级数(?)当z为实变量时,收敛域为[-1,1],但是在实分析中很难求出它的和,本文研究(1)的更一般情形,即把z看成复变量,我们利用复分析的方法,求出(1)的和F(z),并证明F(z)在单位圆盘|z|<1内单叶,同时,导出F(z),F(z)的模的估计,以及其它的一些不等式。

This paper has studied simpler form for (?) that that is z is regarded as complex variable.The method of complex analysis is used to get the sum of(1)and F(z) is testified to be simple leaf in unit round plate |z|<1, mean- while,the modular estimation of F(z)and F(z)as well as some other inequalities are derived.