Skew-orthogonal polynomials for a quartic Freud weight: two classes of quasi-orthogonal polynomials
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913059227828224 |
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| author | Benassi, Costanza Dell'Atti, Marta |
| author_facet | Benassi, Costanza Dell'Atti, Marta |
| contents | This work is a thorough investigation of skew-orthogonal polynomials with respect to a quartic Freud weight. We provide an explicit method to evaluate skew-orthogonal polynomials of any degree as linear combinations of orthogonal polynomials. The coefficients of these combinations can be evaluated via novel recursive relations. Moreover, we observe that skew-orthogonal polynomials with even and odd degree constitute two families of quasi-orthogonal polynomials with respect to two different semi-classical Laguerre weights, and we provide the first instance of closed recursive relations involving skew-orthogonal polynomials only. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22616 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Skew-orthogonal polynomials for a quartic Freud weight: two classes of quasi-orthogonal polynomials Benassi, Costanza Dell'Atti, Marta Classical Analysis and ODEs Mathematical Physics Exactly Solvable and Integrable Systems 33D45 (Primary) 42C05, 82B99 (Secondary) This work is a thorough investigation of skew-orthogonal polynomials with respect to a quartic Freud weight. We provide an explicit method to evaluate skew-orthogonal polynomials of any degree as linear combinations of orthogonal polynomials. The coefficients of these combinations can be evaluated via novel recursive relations. Moreover, we observe that skew-orthogonal polynomials with even and odd degree constitute two families of quasi-orthogonal polynomials with respect to two different semi-classical Laguerre weights, and we provide the first instance of closed recursive relations involving skew-orthogonal polynomials only. |
| title | Skew-orthogonal polynomials for a quartic Freud weight: two classes of quasi-orthogonal polynomials |
| topic | Classical Analysis and ODEs Mathematical Physics Exactly Solvable and Integrable Systems 33D45 (Primary) 42C05, 82B99 (Secondary) |
| url | https://arxiv.org/abs/2604.22616 |