# Marko Petkovšek: Definite Sums as Solutions of Linear Recurrences

Date: 10. 12. 2017

Source: Discrete mathematics seminar

Source: Discrete mathematics seminar

Torek, 12. 12. 2017, od 10h do 12h, Predavalnica 3.07 , Jadranska 21

**Povzetek.**Holonomic sequences are those which satisfy a homogeneous linear recurrence with polynomial coefficients. Several algorithms are known which find solutions of such recurrences within some class of explicitly representable sequences (e.g., polynomial, rational, hypergeometric, d'Alembertian, Liouvillian). These classes do not exhaust explicitly representable holonomic sequences. For instance, every definite hypergeometric sum on which Zeilberger's Creative Telescoping algorithm succeeds is a holonomic sequence, but many such sequences are not even Liouvillian. Therefore it makes sense to consider what one might call the "inverse Zeilberger's problem": given a homogeneous linear recurrence with polynomial coefficients, find its solutions representable as definite sums of a certain class. Here we make a (tiny) first step in this direction.