Nonlinear Phenomena in Complex Systems, 2026, Vol.29, No.3, pp.280

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2026, Vol.29, No.3, pp.280 - 291

Some Mathematical Methods Relevant to Analytical Calculations of Anomalous Magnetic Moments of Leptons

L. P. Kaptari, V. I. Lashkevich, and O. P. Solovtsova

The mathematical methods and approaches used in our analytical calculations of electromagnetic corrections to the leptonic anomaly a_L, which is caused by a special class of Feynman diagrams with insertions of the vacuum polarization operator, are presented and examined in detail. The developed methods are essentially based on the Mellin--Barnes transform for the propagators of massive particles with subsequent application of the PSLQ algorithm to solve the emerging functional equations. Functional equations are also used in the procedure of analytic continuation of a particular type of hypergeometric functions to the entire complex plane of their parameters. It is shown that these approaches make it possible to obtain explicit expressions for radiative corrections of rather high orders.

Key words: lepton anomaly, radiative corrections, high orders, Mellin--Barnes transform, analytic continuation

DOI: https://doi.org/10.5281/zenodo.23284664

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