Determinantal Formulas for Exceptional Orthogonal Polynomials
We present determinantal formulas for families of exceptional ₘ-Laguerre and exceptional ₘ-Jacobi polynomials and also for exceptional ₂-Hermite polynomials. The formulas resemble Vandermonde determinants and use the zeros of the classical orthogonal polynomials.
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2022 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2022
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211621 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Determinantal Formulas for Exceptional Orthogonal Polynomials. Brian Simanek. SIGMA 18 (2022), 047, 16 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862706722232074240 |
|---|---|
| author | Simanek, Brian |
| author_facet | Simanek, Brian |
| citation_txt | Determinantal Formulas for Exceptional Orthogonal Polynomials. Brian Simanek. SIGMA 18 (2022), 047, 16 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present determinantal formulas for families of exceptional ₘ-Laguerre and exceptional ₘ-Jacobi polynomials and also for exceptional ₂-Hermite polynomials. The formulas resemble Vandermonde determinants and use the zeros of the classical orthogonal polynomials.
|
| first_indexed | 2026-03-19T02:36:27Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211621 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T02:36:27Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Simanek, Brian 2026-01-07T13:39:36Z 2022 Determinantal Formulas for Exceptional Orthogonal Polynomials. Brian Simanek. SIGMA 18 (2022), 047, 16 pages 1815-0659 2020 Mathematics Subject Classification: 42C05; 33C47 arXiv:2202.01278 https://nasplib.isofts.kiev.ua/handle/123456789/211621 https://doi.org/10.3842/SIGMA.2022.047 We present determinantal formulas for families of exceptional ₘ-Laguerre and exceptional ₘ-Jacobi polynomials and also for exceptional ₂-Hermite polynomials. The formulas resemble Vandermonde determinants and use the zeros of the classical orthogonal polynomials. It is a pleasure to thank Rob Milson for the helpful discussion about the content of this work. The author gratefully acknowledges support from the Simons Foundation through a collaboration grant 707882. The author also thanks the anonymous referees for their useful feedback. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Determinantal Formulas for Exceptional Orthogonal Polynomials Article published earlier |
| spellingShingle | Determinantal Formulas for Exceptional Orthogonal Polynomials Simanek, Brian |
| title | Determinantal Formulas for Exceptional Orthogonal Polynomials |
| title_full | Determinantal Formulas for Exceptional Orthogonal Polynomials |
| title_fullStr | Determinantal Formulas for Exceptional Orthogonal Polynomials |
| title_full_unstemmed | Determinantal Formulas for Exceptional Orthogonal Polynomials |
| title_short | Determinantal Formulas for Exceptional Orthogonal Polynomials |
| title_sort | determinantal formulas for exceptional orthogonal polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211621 |
| work_keys_str_mv | AT simanekbrian determinantalformulasforexceptionalorthogonalpolynomials |