Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction

• 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
• 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.

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...