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In this work we present the computer algebra package HarmonicSums and itstheoretical background for the manipulation of harmonic sums and some relatedquantities as for example Euler-Zagier sums and harmonic polylogarithms.Harmonic sums and generalized harmonic sums emerge as special cases ofso-called d'Alembertian solutions of recurrence relations. We show thatharmonic sums form a quasi-shuffle algebra and describe a method how we canfind algebraically independent harmonic sums. In addition, we define adifferentiation on harmonic sums via an extended version of the Mellintransform. Along with that, new relations between harmonic sums will arise.Furthermore, we present an algorithm which rewrites certain types of nestedsums into expressions in terms of harmonic sums. We illustrate by nontrivialexamples how these algorithms in cooperation with the summation package Sigmasupport the evaluation of Feynman integrals.

A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics