Bonn 2010 – wissenschaftliches Programm
T 12.5: Vortrag
Mittwoch, 17. März 2010, 15:00–15:15, HG XVI
A Toolbox for Harmonic Sums and their Analytic Continuations — •Jakob Ablinger1, Johannes Bluemlein2, and Carsten Schneider1 — 1RISC, J. Kepler University, Linz, Austria — 2DESY, Zeuthen, Germany
The package HarmonicSums implemented in the computer algebra system Mathematica is presented. It supports higher loop calculations in QCD and QED to represent single-scale quantities like anomalous dimensions and Wilson coefficients. The package allows to reduce general harmonic sums due to their algebraic and different structural relations. We provide a general framework for these reductions and the explicit representations up to weight w=8. For the use in experimental analyzes we also provide an analytic formalism to continue the harmonic sums form their integer arguments into the complex plane, which includes their recursions and asymptotic representations. The main ideas are illustrated by specific examples.