Theory of Analytic Continuation and Its Applications in Modern Complex Analysis

Abstract

This paper explores recent advancements in the theory of analytic continuation and their implications for modern complex analysis. Analytic continuation, a method for extending the domain of a given analytic function, has undergone significant developments, enhancing our understanding of complex functions and their behaviors. We review classical approaches to analytic continuation, including the role of power series and the monodromy theorem, and introduce contemporary techniques involving sheaf theory and Riemann surfaces. Additionally, we investigate the applications of these advancements in various domains, such as the solution of differential equations, the study of singularities, and the analytic properties of special functions. Emphasis is placed on the interplay between theoretical insights and practical applications, demonstrating how modern tools in analytic continuation contribute to solving complex problems in mathematics and physics.

Cite as:

A.D. Awasare. (2024). Theory of Analytic Continuation and Its Applications in Modern Complex Analysis. Journal of Applied Mathematics and Statistical Analysis, 5(3), 1–3. 

https://doi.org/10.5281/zenodo.13235127