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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| Дата: | 2007 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2007
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
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irk-123456789-1478322019-02-17T01:27:52Z Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction Vinet, L. Zhedanov, A. 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. 2007 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147832 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Vinet, L. Zhedanov, A. |
| spellingShingle |
Vinet, L. Zhedanov, A. Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Vinet, L. Zhedanov, A. |
| author_sort |
Vinet, L. |
| title |
Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction |
| title_short |
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_sort |
elliptic biorthogonal polynomials connected with hermite's continued fraction |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147832 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT vinetl ellipticbiorthogonalpolynomialsconnectedwithhermitescontinuedfraction AT zhedanova ellipticbiorthogonalpolynomialsconnectedwithhermitescontinuedfraction |
| first_indexed |
2023-05-20T17:28:37Z |
| last_indexed |
2023-05-20T17:28:37Z |
| _version_ |
1796153390474985472 |