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SIGMA 3 (2007), 003, 18 pages math.CA/0701135
https://doi.org/10.3842/SIGMA.2007.003
Contribution to the Vadim Kuznetsov Memorial Issue
Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction
Luc Vinet a and Alexei Zhedanov b
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
Received October 07, 2006, in final form December
12, 2006; Published online January 04, 2007
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 Szegö polynomials orthogonal on the unit
circle. Relations with associated Legendre polynomials are
considered.
Key words:
Laurent biorthogonal polynomials; associated Legendre polynomials; elliptic integrals.
pdf (266 kb)
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