We investigate ε-factorised differential equations, uniform transcendental weight and purity for Feynman integrals. We are in particular interested in Feynman integrals beyond the ones which evaluate to multiple polylogarithms. We show that a ε-factorised differential equation does not necessarily lead to Feynman integrals of uniform transcendental weight. We also point out that a proposed definition of purity works locally, but not globally.
@article{arxiv.2301.02264,
title = {On $\varepsilon$-factorised bases and pure Feynman integrals},
author = {Hjalte Frellesvig and Stefan Weinzierl},
journal= {arXiv preprint arXiv:2301.02264},
year = {2024}
}