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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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2007
Main Authors: Vinet, L., Zhedanov, A.
Format: Article
Language:English
Published: Інститут математики НАН України 2007
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147832
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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.
first_indexed 2025-11-24T04:39:12Z
format Article
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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
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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