Reclassifying Feynman integrals as special functions

TL;DR

This paper proposes a novel perspective by defining Feynman integrals as a new class of special functions, enabling systematic calculation and opening new research avenues in mathematical physics.

Contribution

It introduces the idea of classifying Feynman integrals as special functions, facilitating their systematic computation and theoretical understanding.

Findings

Feynman integrals can be systematically calculated using the AMFlow method.

Defining Feynman integrals as special functions offers new theoretical insights.

Outlines key directions for future research in this area.

Abstract

Although Feynman integrals in general cannot be expressed as well-studied special functions, they can be calculated systematically and efficiently using the \texttt{AMFlow} method in combination with differential equations in the kinematic space. Therefore, it is constructive to define Feynman integrals as a new class of special functions (or transcedental numbers if there is no kinematic variable). Several crucial avenues for further exploration in this direction are outlined.