On a procedure to derive $\epsilon$-factorised differential equations beyond polylogarithms

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In this manuscript, we elaborate on a procedure to derive $\epsilon$-factorised differential equations for multi-scale, multi-loop classes of Feynman integrals that evaluate to special functions beyond multiple polylogarithms.

• We demonstrate the applicability of our approach to diverse classes of problems, by working out $\epsilon$-factorised differential equations for single- and multi-scale problems of increasing complexity.
• To start we are reconsidering the well-studied equal-mass two-loop sunrise case, and move then to study other elliptic two-, three- and four-point problems depending on multiple different scales.
• Finally, we showcase how the same approach allows us to obtain $\epsilon$-factorised differential equations also for Feynman integrals that involve geometries beyond a single elliptic curve.