arXiv math/07011352007-01-04math.CAmath-phmath.MP

Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction

Luc Vinet, Alexei Zhedanov

备注：: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
发表信息：: SIGMA 3 (2007), 003, 18 pages
DOI：: 10.3842/SIGMA.2007.003

英文摘要：

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.

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