RESUMMATION OF DIVERGENT SERIES IN QUANTUM FIELD THEORY: BESSEL, HYPERGEOMETRIC AND MEIJER G-FUNCTIONS

The present study explores resummation of the divergent series in perturbative expansions using transformation techniques, using Bessel and hypergeometric function representations, to improve the convergence of transformed series. The mathematical results are evaluated introducing Hankel transforms for resummation. The study focuses on expressing the transformations regarding hypergeometric functions and extends the analysis to the Meijer-G function. The efficiency is demonstrated through numerical computations, where the transformed series are compared with known Borel summation techniques. The applications of the methods in quantum field theory are discussed, highlighting their role in extracting meaningful physical predictions from perturbative expansions.