Iterated integrations of complete elliptic integrals

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.