This thesis explores the application of Padé and D-Log Padé approximants in Quantum Chromodynamics (QCD), focusing on their potential to model divergent functions while maintaining essential analytical properties. We propose a new convergence conjecture for D-Log Padé approximants in the case of Stieltjes functions and perform a comparative analysis of both techniques across several QCD-related scenarios. These include determining the anomalous magnetic moment of the muon, parameterising form factors in B-meson decays, and studying the pion form factor. Our findings demonstrate the effectiveness of these approximants in reducing uncertainties and improving parameterisations of expressions with poles or branch cuts.
Supervisor: Pere Masjuan