Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction - Vinet, L.; Zhedanov, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
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.