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arXiv · 2205.15182

Analytic continuation of harmonic sums: dispersion representation

V. N. Velizhanin
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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.

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V. N. Velizhanin. 2022-05-30. Analytic continuation of harmonic sums: dispersion representation. https://doi.org/10.1016/j.nuclphysb.2022.115976

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