Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction

Abstract

We study a family of the Laurent biorthogonal polynomials arising from the Her- mite 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 Szego polynomials orthogonal on the unit circle. Relations with associated Legendre polynomials are considered.