TL;DR
This paper introduces a straightforward dispersion-based method for the analytic continuation of nested harmonic sums to complex arguments, enabling accurate numerical evaluations from a precomputed database of pole expressions.
Contribution
It provides a novel dispersion representation for nested harmonic sums and details a procedure for their precise numerical evaluation.
Findings
Dispersion representation effectively extends harmonic sums to complex arguments.
Numerical evaluation method achieves high precision.
Database of pole expressions facilitates the approach.
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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