Christoph Koutschan: Holonomic function identities

Christoph Koutschan
Research Institute for Symbolic Computation (RISC)
Linz

Povzetek: Since Zeilberger's pioneering work in the early 1990's lots of progress has been made in the algorithmic treatment of holonomic function identities (this class includes a wide variety of special functions as well as their integrals and sums). As major achievements we want to mention the introduction of Ore algebras as a unifying framework, Takayama's algorithm for the integration of modules and Chyzak's creative telescoping algorithm. We will give an overview over the theory and demonstrate our new Mathematica implementation of the related algorithms. This software was already successfully applied to prove an open conjecture from combinatorics, to find formulae that are needed for finite element methods, and to check correctness of omplicated special function identities.