Christoph Koutschan (Johann Radon Institute for Computational and Applied Mathematics, Austria)

Computer algebra with D-finite functions

Thursday, 20 June 2024, 16:00-17:00 in HG00.622

Abstract

D-finite functions play a prominent role in computer algebra because they are well suited for representation in a symbolic software system, and because they include many functions of interest, such as special functions, orthogonal polynomials, generating functions, etc. For studying the integral or the summation of a D-finite function, one may use the method of creative telescoping. This method has been systematically introduced by Zeilberger in the 1990s. Since then it has found many applications in statistical physics, combinatorics, algebraic statistics, number theory, etc., by its abilities to prove special function identities, to extract asymptotic information, and to evaluate determinants. In this lecture, we briefly explain the underlying theory and present some of its applications.