Regular Seminar Carsten Schneider (RISC)
room G.O. Jones 610
Symbolic summation started with Abramov's telescoping algorithm for rational functions (1971), was pushed further by Gosper's algorithm for hypergeometric expressions (1978) and reached its first peak level with Zeilberger's creative telescoping algorithm (1990) and Petkovsek's recurrence solver (1992) to treat definite hypergeometric sums. In this talk we focus on the difference ring approach which covers all these algorithms as special cases. Its foundation was lead by Karr's summation algorithm (1981) and has been pushed forward significantly within the last 18 years. In a long term project with DESY (Deutsches Elektronen-Synchrotron) the produced algorithms have been playing a central role to evaluate several hundred thousands of 2-loop and 3-loop massive Feynman integrals. In this talk we will elaborate by concrete examples how our advanced difference ring theory and the underlying algorithms encoded within the summation package Sigma are used to attack these highly complicated Feynman integrals.