Summation Theory of Difference Rings and Applications - Lecture 3

In this third lecture of a mini-course on summation theory, Professor Carsten Schneider concludes his exploration of difference rings and their applications. Building upon the previous lectures, learn how the summation package Sigma can be applied to solve complex problems in enumerative combinatorics, number theory, and elementary particle physics. The lecture demonstrates practical applications of the theoretical framework established earlier, showing how indefinite nested sums defined over nested products can be manipulated using parameterized telescoping and recurrence solving techniques. Discover how the difference ring setting provides a powerful toolbox for constructing summation objects with algebraically independent sequences. Recorded during the thematic meeting "Enumerative combinatorics and effective aspects of differential equations" on February 27, 2025, at the Centre International de Rencontres Mathématiques in Marseille, France. Access this video and other mathematical talks on CIRM's Audiovisual Mathematics Library, featuring helpful functionalities like chapter markers, keywords, abstracts, bibliographies, and multi-criteria search options.