Analytic continuation of harmonic sums: dispersion representation

Abstract

We present a simple representation for analytically continued nested harmonic sums for the arbitrary complex argument. This representation can be obtained for a wide range of nested harmonic sums from a precomputed database for the pole expressions of these sums near negative integers. We describe the procedure for the precise numerical evaluations of the corresponding results from the dispersion representation.

Comments: 12 pages, 3 ancillary files, typos corrected, links to GitHub added, references added