LSJK - a C++ library for arbitrary-precision numeric evaluation of the generalized log-sine functions

TL;DR

The paper addresses the numerical evaluation of generalized log-sine functions that arise in epsilon expansions of Feynman diagrams. It introduces the lsjk C++ library, built on the CLN arbitrary-precision framework, which computes Ls_j^(k)(θ) for 0<θ<π using rigorous series representations and supports k≤9 (up to weight 11, with extension paths). It also documents rich mathematical structure, including identities linking generalized log-sine functions to Clausen and Nielsen polylogarithms and provides explicit series representations and special-value relations. The work includes installation details, benchmarks, cross-checks against reference implementations, and a practical example program to demonstrate high-precision evaluation, enabling precise computations in high-energy physics contexts.

Abstract

Generalized log-sine functions appear in higher order epsilon-expansion of different Feynman diagrams. We present an algorithm for numerical evaluation of these functions of real argument. This algorithm is implemented as C++ library with arbitrary-precision arithmetics for integer 0 < k < 9 and j > 1. Some new relations and representations for the generalized log-sine functions are given.