Abstract：
In mathematics study series expressed by function terms occupy the important position, the uniform convergence of series expressed by function terms in series theory is the most fundamental and most important problem. Uniform convergence is an important property of series expressed by function terms, in order to further study the properties of series expressed by function terms, effective discriminant function of uniform convergence of the series is very important. In this paper, several series discriminant function method and the common term series discriminant method, on the basis of proposed criterion series expressed by function terms of popularization and application. So in this paper, starting from the definition of series expressed by function terms, a series of common function criterion for promotion, mainly summarized summarizes the Cauchy uniform convergence criterion, M discriminant theorem, discriminant method of optimal discriminant method and other series of popularization and application. Hope that through this article gives the discriminant method of popularization and application, the discriminant of uniform convergence series expressed by function terms provides convenient.
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