Coefficients Calculation of Laurent Series in the Neighborhood of Complex Variable Function Poles

Abstract

The theory of complex function is a key part of mathematics, which can solve the complex problems in production and life. It is of great significance to extend the research field of complex function theory. In this paper, taking a complex variable function as the research object, a calculation method of Laurent series coefficient of complex function pole neighborhood expansion was proposed to determine the complex variable function pole, determine the order of complex variable function pole, calculate the residue of high-order pole in complex variable function, thus judging the attribute of complex variable function. In this regard, the coefficient formula was used to calculate the coefficients of Laurent series in the neighborhood of the complex variable function poles.