Fractions of Recurrence Operators for Generalized Fourier Series in Classical Orthogonal Polynomials
Classical Analysis and ODEs
2026-04-30 v1 Symbolic Computation
Abstract
We consider series expansions in bases of classical orthogonal polynomials. When such a series solves a linear differential equation with polynomial coefficients, its coefficients satisfy a linear recurrence equation. We interpret this equation as the numerator of a fraction of linear recurrence operators. This interpretation lets us give a simple and unified view of previous algorithms computing these recurrences, with a noncommutative Euclidean algorithm as the algorithmic engine. Finally, we demonstrate the effectiveness of our approach on various examples.
Keywords
Cite
@article{arxiv.2604.26944,
title = {Fractions of Recurrence Operators for Generalized Fourier Series in Classical Orthogonal Polynomials},
author = {Alexandre Benoit and Nicolas Brisebarre and Bruno Salvy},
journal= {arXiv preprint arXiv:2604.26944},
year = {2026}
}