THE USE OF DIFFERENTIAL REDUCTION OF GENERALISED HYPERGEOMETRIC FUNCTIONS TO FEYNMAN DIAGRAMS: ONE-VARIABLE CASE

Abstract

Using Feynman diagrams as a framework, this study investigates the one-variable scenario of applying differential reduction methods to generalised hypergeometric functions. An essential part of quantum field theory for computing scattering amplitudes and other physical variables are generalised hypergeometric functions, which are used often in the assessment of Feynman integrals. Reduced integrals provide for more efficient computing and analytical investigation by simplifying multivariable integrals into one-variable forms. Our investigation delves deep into the strategies used to accomplish this reduction, shedding light on crucial stages and mathematical transformations. By providing concrete instances, we show how these methods streamline the calculation of Feynman diagrams, which in turn advances the real-world relevance of theoretical physics. Based on the findings, differential reduction might be used more widely in several branches of computer mathematics and high-energy physics.