Exploring the linear space of Feynman integrals via generating functions
Xin Guan, Xiang Li, Yan-Qing Ma · Physical review. D/Physical review. D. · 2023
Deriving a comprehensive set of reduction rules for Feynman integrals has been a long-standing challenge. In this paper, we present a proposed solution to this problem utilizing generating functions of Feynman integrals. By establishing and solving differential equations of these generating functions, we are able to derive a system of reduction rules that effectively reduce any associated Feynman integrals to their bases. We illustrate this method through various examples and observe its potential value in numerous scenarios.