Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction

Details Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction

2007-01-04

arxiv.org/abs/math/0701135v1

SIGMA 3 (2007), 003, 18 pages

Mathematics

Classical Analysis and ODEs

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2007.003

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 Szeg\"o polynomials orthogonal on the unit circle. Relations with associated Legendre polynomials are considered.

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