该级数一致收敛于收敛环内的紧子集上。

The series converges uniformly on compact subsets of the interior of the annulus of convergence.

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第二部分是在一致收敛条件下函数列、函数项级数以及含参量反常积分的性质。

The second part is in uniform convergence conditions function series, function and parameter improper integral. We properties.

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对于函数级数，研究其和函数的解析性质很重要，但函数级数必须具有一致收敛性，而判断函数级数的一致收敛性往往是比较困难的。

However, this study should be based on the fact that the series must have consistent convergence, the judgment of which is rather difficult.

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