Title: An introduction to symbolic summation and integration
Speaker: Flavia Stan, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria
Location: 2:30-3:20 on December 10, 2010 in Savery Hall 157
I will give a short overview of symbolic summation and integration methods including many examples. These methods are used to algorithmically find and prove identities involving sums, products and integrals over certain classes of special functions.
While the integration case can be traced back to the work of Liouville (1833) and the algorithms of Risch (1969) and Trager (1984), the first generic approach to summation problems was presented by Sister Celine Fasenmyer in her thesis from 1945. Later, Gosper’s algorithm (1978) for indefinite summation which he implemented in Macsyma became a cornerstone of the field and made it popular as part of an emerging interest in computer mathematics systems.
As a result of the latest theoretical advances and their implementations in mainstream computer algebra systems, summation and integration methods became strong enough for real-world applications. For instance, I will present new applications of Wilf-Zeilberger methods to the computation of Feynman integrals from a cooperation project between RISC and DESY.