Numerical evaluation of iterated integrals related to elliptic Feynman integrals

Abstract

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,τ). For the Kronecker coefficient functions iterated integrals in dτ and dz are implemented. This includes elliptic multiple polylogarithms. Program summaryNote: The program uploaded to the CPC Library is the full GiNaC program, original authors C. Bauer, A. Frink and R. Kreckel. The algorithms described in this article are integrated into GiNaC.Program title:GiNaC_elipticFeynmanCPC Library link to program files:https://doi.org/10.17632/8vyydbc7zw.1Developer's repository link:https://www.ginac.de/Licensing provisions: GNU General Public License version 2Programming language:C++Other programs called: CLN library, available from https://www.ginac.de/CLN.Nature of problem: Numerical evaluation of iterated integrals related to elliptic Feynman integrals.Solution method: Removal of trailing zeros followed by series expansion.