A Study To Investigate One-Variable Feyman Diagrams Based On Differential Reduction Of Hypergeometric Functions

Abstract

Applying differential reduction techniques to generalised hypergeometric functions in a one-variable situation is examined in this article using Feynman diagrams as a framework. It is standard practice to employ generalised hypergeometric functions for evaluating Feynman integrals. Because of their central role in computing scattering amplitudes and other physical variables, these functions are fundamental to quantum field theory. One way to improve computational and analytical efficiency is to reduce the number of variables used in integrals from several to one. The basic processes and mathematical transformations needed to achieve this reduction are illuminated by our analysis, which thoroughly examines the approaches. By providing concrete instances that show how these methods streamline the computation of Feynman diagrams, we prove that these methods expand the real-world relevance of theoretical physics. The results suggest that differential reduction might emerge as a powerful tool in several areas of computer mathematics and high-energy physics.