AN EXAMPLE OF ONE-VARIABLE FEYNMAN DIAGRAMS BASED ON DIFFERENTIAL REDUCTION OF GENERATED HYPERGEOMETRIC FUNCTIONS

Abstract

This article makes use of Feynman diagrams as a framework in order to investigate the one-variable scenario of applying differential reduction methods to generalised hypergeometric functions. When evaluating Feynman integrals, it is common practice to make use of generalised hypergeometric functions. These functions are essential in quantum field theory, since they are used to compute scattering amplitudes and other physical variables. Integrals that include many variables may be simplified to a single variable, which results in an increase in both computational and analytical efficiency. Our investigation investigates the procedures in great depth, shedding light on the essential processes and mathematical transformations that are required to accomplish this reduction. Through the presentation of particular examples that demonstrate how these strategies simplify the computing of Feynman diagrams, we demonstrate how these techniques increase the practical application of theoretical physics. Based on the findings, it seems that differential reduction might potentially find more applications in a variety of fields within the realms of computer mathematics and high-energy physics.