Mastering Complex Integrals in Multidimensional Spaces:Generalized Theorems and Broad Applications

Abstract

This study presents a pioneering approach in the realm of complex analysis, focusing on the transformation of integrals that involve analytic functions in multi-dimensional complex variable spaces. At the core of our investigation are integrals characterized by functions evaluated across a spectrum of complex arguments, especially around points in n-dimensional real spaces. This research progresses mathematical understanding by advancing intricate derivations and building upon foundational work in the field. A significant aspect of our findings lies in the deep exploration of structures and interrelationships within complex integrals. Additionally, we highlight the substantial impact of this novel methodology on solving complex problems, particularly in the realm of Partial Differential Equations (PDEs). This innovative approach has far-reaching implications, promising to revolutionize problem-solving techniques in mathematical and physical sciences, and paving the way for advanced solutions in complex PDEs and other related areas.