TL;DR
This paper introduces a method to compute nested harmonic sums for any complex argument with arbitrary precision, leveraging their relation to Hurwitz zeta functions, and provides an implementation program.
Contribution
It presents a novel approach connecting harmonic sums to Hurwitz zeta functions for accurate complex argument calculations, including a practical implementation.
Findings
Accurate calculation of harmonic sums for all complex arguments.
Established a relation between harmonic sums and Hurwitz zeta functions.
Provided a software implementation for the method.
Abstract
We present a method for calculating any (nested) harmonic sum to arbitrary accuracy for all complex values of the argument. The method utilizes the relation between harmonic sums and (derivatives of) Hurwitz zeta functions, which allows a harmonic sum to be calculated as an expansion valid for large values of its argument. A program for implementing this method is also provided.
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