https://doi.org/10.1140/epjs/s11734-025-01995-0
Review
Evaluating Feynman integrals through differential equations and series expansions
1
Centre for Cosmology, Particle Physics and Phenomenology (CP3), Universitè catholique de Louvain, Chemin du Cyclotron, 2, 1348, Louvain-la-Neuve, Belgium
2
Dipartimento di Fisica “Aldo Pontremoli”, University of Milano and INFN, Sezione di Milano, 20133, Milan, Italy
a
tommaso.armadillo@uclouvain.be
Received:
25
February
2025
Accepted:
29
September
2025
Published online:
13
October
2025
We review the method of differential equations for the evaluation of multi-loop Feynman integrals. In particular, we focus on the series expansion approach for solving the system of differential equation and we discuss how to perform the analytical continuation of the result to the entire (complex) phase-space. This approach allows us to consider arbitrary internal complex masses. This review is based on a lecture given by the author at the ‘Advanced School & Workshop on Multiloop Scattering Amplitudes’ held in NISER, Bhubaneswar (India) in January 2024.
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
