Computer Algebra Algorithms for Special Functions in Particle Physics

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This work deals with special nested objects arising in massive higher order perturbative calculations in renormalizable quantum field theories.

• On the one hand we work with nested sums such as harmonic sums and their generalizations (S-sums, cyclotomic harmonic sums, cyclotomic S-sums) and on the other hand we treat iterated integrals of the Poincar\'e and Chen-type, such as harmonic polylogarithms and their generalizations (multiple polylogarithms, cyclotomic harmonic polylogarithms).
• The iterated integrals are connected to the nested sums via (generalizations of) the Mellin-transformation and we show how this transformation can be computed.
• We derive algebraic and structural relations between the nested sums as well as relations between the values of the sums at infinity and connected to it the values of the iterated integrals evaluated at special constants.