Elliptic Feynman integrals and pure functions

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We propose a variant of elliptic multiple polylogarithms that have at most logarithmic singularities in all variables and satisfy a differential equation without homogeneous term.

• We investigate several non-trivial elliptic two-loop Feynman integrals with up to three external legs and express them in terms of our functions.
• We observe that in all cases they evaluate to pure combinations of elliptic multiple polylogarithms of uniform weight.
• This is the first time that a notion of uniform weight is observed in the context of Feynman integrals that evaluate to elliptic polylogarithms.