%A HU Guang-ming, LONG Jian-ren
%T Application of the covering space in the complex integral of multiply connected domains
%0 Journal Article
%D 2017
%J Journal of East China Normal University(Natural Science)
%R 10.3969/j.issn.1000-5641.2017.04.006
%P 64-70
%V
%N 4
%U {https://xblk.ecnu.edu.cn/CN/abstract/article_25422.shtml}
%8 2017-07-25
%X It is well known that the integral with variable upper limit of analytic function is a single value function in the simple connected domain, while the integral with variable upper limit of analytic function in the multiply connected domains is as following: _{z0}^{z}*f*(*ζ*)*dζ*, *F*(*z*) is not only dependent on the *z* (*z*_{0} is the fixed point in *D*), but also depends on the integral path and function *f*(*z*) being exact or not in every hole. Therefore *F*(*z*) is likely to be multiple valued function. In this paper, we give a new proof method about the integral of analytic function *f*(*z*) in the multiply connected domain by the regular covering surface.