Numerical evaluation of iterated integrals related to elliptic Feynman integrals

We report on an implementation within GiNaC to evaluate iterated integrals related to elliptic Feynman integrals numerically to arbitrary precision within the region of convergence of the series expansion of the integrand. The implementation includes iterated integrals of modular forms as well as iterated integrals involving the Kronecker coefficient functions g((k))(z, tau). For the Kronecker coefficient functions iterated integrals in d tau and dz are implemented. This includes elliptic multiple polylogarithms. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This study presents an implementation within GiNaC to numerically evaluate iterated integrals related to elliptic Feynman integrals to arbitrary precision within the region of convergence of the series expansion of the integrand.