# EXPANDING THE LAURENT SERIES WITH ITS APPLICATIONS

## Keywords:

Laurent series, integral, contour, applications, singularities.## Abstract

cIn Nepal, there are many mathematics subjects taught at university level. Among them, complex analysis is the most powerful. In complex analysis, the Laurent series expansion is a well-known subject because it may be used to find the residues of complex functions around their singularities. It turns out that computing the Laurent series of a function around its singularities is an effective way to calculate the integral of the function along any closed contour around the singularities as well as the residue of the function. Learning the Laurent series concepts can be difficult, and many students struggle to develop adequate understanding, reasoning, and problem-solving skills. Therefore, this article presents multiple practical examples where the Laurent series of a function is found and then utilized to compute the integral of the function over any closed contour around the singularities of the function, based on the theory of the Laurent series.