Fractions of Recurrence Operators for Generalized Fourier Series in Classical Orthogonal Polynomials
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918474663591936 |
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| author | Benoit, Alexandre Brisebarre, Nicolas Salvy, Bruno |
| author_facet | Benoit, Alexandre Brisebarre, Nicolas Salvy, Bruno |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26944 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fractions of Recurrence Operators for Generalized Fourier Series in Classical Orthogonal Polynomials Benoit, Alexandre Brisebarre, Nicolas Salvy, Bruno Classical Analysis and ODEs Symbolic Computation Primary 33C45, 33F10, 42C05, 42C10, 65D15, 65Q05, 68W30, Secondary 33C20, 65L99 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. |
| title | Fractions of Recurrence Operators for Generalized Fourier Series in Classical Orthogonal Polynomials |
| topic | Classical Analysis and ODEs Symbolic Computation Primary 33C45, 33F10, 42C05, 42C10, 65D15, 65Q05, 68W30, Secondary 33C20, 65L99 |
| url | https://arxiv.org/abs/2604.26944 |