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.

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

References in corpus (2)

• Iterated Binomial Sums and their Associated Iterated Integrals
• Analytic continuation of the Mellin moments of deep inelastic structure functions

Cited by in corpus (3)

• Multi-Collinear Splitting Kernels for Track Function Evolution
• Anomalous dimensions at small spins
• Analytic continuation of harmonic sums with purely imaginary indices near the integer values