Apply the contour integral on multivalued function from the complex plane

Abstract

This paper mainly intends to integrate the multivalued function on the complex plane by using contour integral. The improper integral of a single-valued function on the real plane is often difficult to solve directly. In addition to solving the integral itself, we also need to judge its convergence and divergence. In order to solve integral of this kind, this paper extends its domain onto the complex plane. Then, we can find that this kind of function may become a complex multivalued function on the complex plane. However, if we use the contour integral, we can deal with the complex-valued function efficiently and then obtain the solution of the integral. Using contour integral to solve the integral in the complex field is applied in many fields. Contour integral can be used to solve partial differential equations, which can be applied in electrodynamics, quantum mechanics, hydrodynamics, and other fields.