关于经典正交多项式广义傅里叶级数的递推算子分数
经典分析与常微分方程
2026-04-30 v1 符号计算
摘要
我们考虑以经典正交多项式基底的级数展开。当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.
引用
@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}
}