We introduce a class of functions which constitutes an obvious elliptic generalization of multiple polylogarithms. A subset of these functions appears naturally in the ɛ-expansion of the imaginary part of the two-loop massive sunrise graph. Building upon the well known properties of multiple polylogarithms, we associate a concept of weight to these functions and show that this weight can be lowered by the action of a suitable differential operator. We then show how properties and relations among these functions can be studied bottom-up starting from lower weights.
Nuclear Physics B
- Pub Date:
- December 2017
- High Energy Physics - Phenomenology;
- High Energy Physics - Theory
- 27 pages plus three appendices, v2: references added, typos corrected, accepted for publication on NPB