@**mastersthesis**{RISC3851,author = {Jakob Ablinger},

title = {{A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics}},

language = {english},

abstract = {In this work we present the computer algebra package HarmonicSums and its theoretical
background for the manipulation of harmonic sums and some related quantities as
for example Euler-Zagier sums and harmonic polylogarithms. Harmonic sums and
generalized harmonic sums emerge as special cases of so-called d’Alembertian solutions
of recurrence relations. We show that harmonic sums form a quasi-shuffle algebra
and describe a method how we can find algebraically independent harmonic sums. In
addition, we define a differentiation on harmonic sums via an extended version of the
Mellin transform. Along with that, new relations between harmonic sums will arise.
Furthermore, we present an algorithm which rewrites certain types of nested sums into
expressions in terms of harmonic sums. We illustrate by nontrivial examples how these
algorithms in cooperation with the summation package Sigma support the evaluation
of Feynman integrals.},

year = {2009},

month = {February},

translation = {0},

school = {Johannes Kepler University},

length = {0}

}