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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2007-01-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2007/003/ |
| _version_ | 1818789359572221952 |
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| author | Luc Vinet Alexei Zhedanov |
| author_facet | Luc Vinet Alexei Zhedanov |
| author_sort | Luc Vinet |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-18T14:38:19Z |
| format | Article |
| id | doaj.art-7ba00d4659e64740906f0889fc21c582 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-18T14:38:19Z |
| publishDate | 2007-01-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-7ba00d4659e64740906f0889fc21c5822022-12-21T21:04:28ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-01-013003Elliptic Biorthogonal Polynomials Connected with Hermite's Continued FractionLuc VinetAlexei ZhedanovWe 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.http://www.emis.de/journals/SIGMA/2007/003/Laurent biorthogonal polynomialsassociated Legendre polynomialselliptic integrals |
| spellingShingle | Luc Vinet Alexei Zhedanov Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction Symmetry, Integrability and Geometry: Methods and Applications Laurent biorthogonal polynomials associated Legendre polynomials elliptic integrals |
| 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 |
| topic | Laurent biorthogonal polynomials associated Legendre polynomials elliptic integrals |
| url | http://www.emis.de/journals/SIGMA/2007/003/ |
| work_keys_str_mv | AT lucvinet ellipticbiorthogonalpolynomialsconnectedwithhermitescontinuedfraction AT alexeizhedanov ellipticbiorthogonalpolynomialsconnectedwithhermitescontinuedfraction |