example sum

The group Computer Algebra for QFT (team leader: Carsten Schneider) aims at developing flexible and efficient symbolic summation and integration techniques, as well as special function algorithms that assist in the calculation of Feynman integrals arising in the context of Elementary Quantum Field Theory. The group is intimately connected with the Combinatorics Group at RISC.
This goal is attacked in intensive cooperation with the Theory Group of the Deutsches Elektronen Synchrotron DESY, Zeuthen (team leader: Johannes Blümlein). A cooperation contract between the Johannes Kepler University (JKU) and DESY was signed in February 2007 and has been prolonged step-wise till February 2022.

Beyond the application of these methods, algorithms and tools in Quantum Field Theory, the group applies these methods also in other fields, such as combinatorics (simplification of enumerative problems) or number theory (multiple zeta values, irrationality proofs, new relations between sums).
The group takes part in the Special Research Program (SFB, in short for the German name SpezialForschungsBereich) Algorithmic and Enumerative Combinatorics which started in March 2013. It is a special effort of three institutes, the Faculty of Mathematics (University of Vienna), the Institute for Discrete Mathematics and Geometry (Technical University Vienna), and the Research Institute for Symbolic Computation (Johannes Kepler University Linz) funded by the Austrian Science Funds (FWF).