Analytic Continuation of Harmonic Sums

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.

References in corpus (5)

• Implications of CTEQ global analysis for collider observables
• Global analysis of fragmentation functions for pions and kaons and their uncertainties
• AKK Update: Improvements from New Theoretical Input and Experimental Data
• Global Analysis of Fragmentation Functions for Protons and Charged Hadrons
• QCD Corrections to Semi-Inclusive Hadron Production in Electron-Positron Annihilation at Two Loops

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