May 21, 2026 at 10 AM
We study series expansions in bases of classical orthogonal polynominals. When such a series solves a linear differential equation with polynominal coefficients, its coefficients satisfy a linear recurrence equation. We interpret this equation as the numerator of a fraction of linear recurrence operators. This interpretation allows us to provide a simple and unified view of previous algorithms computing these recurrences, with a noncommutative Euclidean algorithm as the agorithmic engine. We will also show how to handle the case of functions with singularities at the endpoints of their domain and we will demonstrate a Maple implementation of our algorithms on a few examples.
Nicolas Brisebarre (LIP, ENS Lyon)
Bâtiment ESPRIT, salle Rubis, 3ème étage
français
English