Carsten Schneider, RISC-Linz (Austria)

Abstract

A major breakthrough in symbolic summation was Doron Zeilberger's creative telescoping method to compute linear recurrences of definite hypergeometric sums. In this talk I will illustrate the algorithmic framework in the setting of difference rings in which one can extend Z's method for summands that are built by indefinite nested sums and products. In combination with a sophisticated recurrence solver one obtains a rather general machinery to simplify big classes of definite multi-sums to expressions in terms of indefinite nested sums and products. The underlying difference ring algorithms implemented in the summation package Sigma will be illustrated by non-trivial applications coming, e.g., from combinatorics and particle physics.

Link to video: https://vimeo.com/611079399

Presented Via Zoom: https://rutgers.zoom.us/j/94346444480

Password: 6564120420

For further information see: https://sites.math.rutgers.edu/~zeilberg/expmath/