Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction
经典分析与常微分方程
2008-04-24 v1 数学物理
math.MP
摘要
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.
引用
@article{arxiv.math/0701135,
title = {Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction},
author = {Luc Vinet and Alexei Zhedanov},
journal= {arXiv preprint arXiv:math/0701135},
year = {2008}
}
备注
This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/