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Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction
Інший ID:
2000 Mathematics Subject Classification: 33C45; 42C05
Посилання:
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.
Підтримка:
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.
Дата:
2007
Переглядів:
509
Завантажень:
257
Анотація:
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.
