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Symmetry, Integrability and Geometry: Methods and Applications, 2007, Volume 3, 003, 18 pp.
DOI: https://doi.org/10.3842/SIGMA.2007.003 (Mi sigma129) 		 
Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction

Luc Vineta, Alexei Zhedanovb

a Université de Montréal, PO Box 6128, Station Centre-ville, Montréal QC H3C 3J7, Canada
b Donetsk Institute for Physics and Technology, Donetsk 83114, Ukraine
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DOI: https://doi.org/10.3842/SIGMA.2007.003
Abstract: 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 Szegő polynomials orthogonal on the unit circle. Relations with associated Legendre polynomials are considered.
Keywords: Laurent biorthogonal polynomials; associated Legendre polynomials; elliptic integrals.
Received: October 7, 2006; in final form December 12, 2006; Published online January 4, 2007
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Document Type: Article
MSC: 33C45; 42C05
Language: English
Citation: Luc Vinet, Alexei Zhedanov, “Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction”, SIGMA, 3 (2007), 003, 18 pp.
Citation in format AMSBIB
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