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Generalized Harmonic, Cyclotomic, and Binomial Sums, their Polylogarithms and Special Numbers
J Ablinger, J Blümlein, C Schneider
A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, sp…
Computer Algebra Algorithms for Special Functions in Particle Physics
Jakob Ablinger
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…
Harmonic Sums, Polylogarithms, Special Numbers, and their Generalizations
Jakob Ablinger, Johannes Blümlein
In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation…
Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms
Jakob Ablinger, Johannes Blümlein, Carsten Schneider
In recent three--loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic s…
Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
Jakob Ablinger, Johannes Blümlein, Carsten Schneider
The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable Quantum Field Theories requires extensions of multiply nested harmonic sums…
A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics
Jakob Ablinger
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 Eu…