Finding Exact Solutions of Linear Recurrences
by
Marko Petkovšek
University of Ljubljana

In the first part of my talk, I will review the algorithms for finding ``nice'' explicit solutions of linear recurrences with polynomial coefficients. These include solutions which are polynomials, rational functions, hypergeometric or q-hypergeometric terms, and Liouvillian functions.

In the second part, I will look at linear recurrences in the multivariate case. While in the univariate case solutions of linear recurrences with constant coefficients have rational generating functions, we show that the multivariate case is much richer: even though initial conditions have rational generating functions, the corresponding solutions can have generating functions which are algebraic but not rational, D-finite but not algebraic, and even non D-finite and non D-algebraic.

Date received: April 22, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caex-65.