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Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction

Luc Vinet·Alexei Zhedanov
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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.

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Luc Vinet, Alexei Zhedanov. 2007-01-04. Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction. https://doi.org/10.3842/sigma.2007.003

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