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: z0zf(ζ)dζ, F(z) is not only dependent on the z (z0 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.
HU Guang-ming
,
LONG Jian-ren
. Application of the covering space in the complex integral of multiply connected domains[J]. Journal of East China Normal University(Natural Science), 2017
, (4)
: 64
-70
.
DOI: 10.3969/j.issn.1000-5641.2017.04.006
[1] 吕以辇, 张学莲. 黎曼曲面[M]. 北京: 科学出版社, 1997.
[2] 聂灵沼, 丁石孙. 代数学引论[M]. 北京: 高等教育出版社, 2010.
[3] 熊金城. 点集拓扑讲义[M]. 北京: 高等教育出版社, 2003.
[4] 余家荣. 复变函数[M]. 北京: 高等教育出版社, 2007.