Methods to Solve Laurent Series of Complex Functions

Abstract

In practical applications, there are always a lot of complex functions, which often make physicists and mathematicians very headache. It is a very important idea to use a polynomial function to approximate a complex function. This paper is about the Laurent series of complex functions, which includes holomorphic functions and meromorphic functions, and tries to derive a general formula or a general way to compute the Laurent series. This paper also includes several basic examples of different types of complex functions and the process to derive the Laurent series of these functions. By finding similarities and summarizing the process, a general method for each or overall function is shown. Examples include common fractional functions, Trigonometric functions, and exponential functions. Some of them include different ways of computing according to it’s characteristics. An analytic function can be extended to a function obtained by analytic extension of the Taylor series defined on an open region on the complex plane, and this method of complex analysis is feasible.