Iterated integrations of complete elliptic integrals

Le résumé fourni par la source

We study an elliptic generalization of multiple polylogarithms that appears naturally in the computation of the imaginary part of the two-loop massive sunrise graph with equal masses. The newly introduced functions fulfill non-homogeneous second order differential equations. As an important result, we introduce a concept of weight associated to the action of the second order differential operator and show how to classify the relations between the functions bottom up in their weight.

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