English

Analytic continuation of harmonic sums: dispersion representation

High Energy Physics - Phenomenology 2022-11-24 v3 High Energy Physics - Theory

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.

Cite

@article{arxiv.2205.15182,
  title  = {Analytic continuation of harmonic sums: dispersion representation},
  author = {V. N. Velizhanin},
  journal= {arXiv preprint arXiv:2205.15182},
  year   = {2022}
}

Comments

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

R2 v1 2026-06-24T11:33:17.549Z