Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction
We study a family of the Laurent biorthogonal polynomials arising from the Hermite continued fraction for a ratio of two complete elliptic integrals. Recurrence coefficients, explicit expression and the weight function for these polynomials are obtained. We construct also a new explicit example of t...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2007 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147832 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction / L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 27 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862532420100685824 |
|---|---|
| author | Vinet, L. Zhedanov, A. |
| author_facet | Vinet, L. Zhedanov, A. |
| citation_txt | Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction / L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 27 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study a family of the Laurent biorthogonal polynomials arising from the Hermite continued fraction for a ratio of two complete elliptic integrals. Recurrence coefficients, explicit expression and the weight function for these polynomials are obtained. We construct also a new explicit example of the Szegö polynomials orthogonal on the unit circle. Relations with associated Legendre polynomials are considered.
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| first_indexed | 2025-11-24T04:39:12Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147832 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T04:39:12Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Vinet, L. Zhedanov, A. 2019-02-16T09:00:30Z 2019-02-16T09:00:30Z 2007 Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction / L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 27 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33C45; 42C05 https://nasplib.isofts.kiev.ua/handle/123456789/147832 We study a family of the Laurent biorthogonal polynomials arising from the Hermite continued fraction for a ratio of two complete elliptic integrals. Recurrence coefficients, explicit expression and the weight function for these polynomials are obtained. We construct also a new explicit example of the Szegö polynomials orthogonal on the unit circle. Relations with associated Legendre polynomials are considered. This paper is a contribution to the Vadim Kuznetsov Memorial Issue “Integrable Systems and Related Topics”. The authors thank to the referees for their remarks leading to improvement of the text. A.Zh. thanks Centre de Recherches Math´ematiques of the Universit´e de Montr´eal for hospitality. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction Article published earlier |
| spellingShingle | Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction Vinet, L. Zhedanov, A. |
| title | Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction |
| title_full | Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction |
| title_fullStr | Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction |
| title_full_unstemmed | Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction |
| title_short | Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction |
| title_sort | elliptic biorthogonal polynomials connected with hermite's continued fraction |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147832 |
| work_keys_str_mv | AT vinetl ellipticbiorthogonalpolynomialsconnectedwithhermitescontinuedfraction AT zhedanova ellipticbiorthogonalpolynomialsconnectedwithhermitescontinuedfraction |