Discussion of Complex integration on Complex Contours

This paper elaborated on the complex integration on the complex contour, and gave the calculation formula of complex integrals according to different cases with different number of singular points, namely, one singular point, n singular points, infinite singular points (countable). Therefore, it is easy to analysis and understand the development and establishment of complex integration on complex contour. Besides, this paper introduced and proved an "improved residue theorem" base on the famous residue theorem, which make it possible to calculate complex integral with countable singular point in an unbounded region.