Elliptic Hypergeometric Laurent Biorthogonal Polynomials with a Dense Point Spectrum on the Unit Circle
Classical Analysis and ODEs
2009-03-19 v2 Exactly Solvable and Integrable Systems
Abstract
Using the technique of the elliptic Frobenius determinant, we construct new elliptic solutions of the -algorithm. These solutions can be interpreted as elliptic solutions of the discrete-time Toda chain as well. As a by-product, we obtain new explicit orthogonal and biorthogonal polynomials in terms of the elliptic hypergeometric function . Their recurrence coefficients are expressed in terms of the elliptic functions. In the degenerate case we obtain the Krall-Jacobi polynomials and their biorthogonal analogs.
Cite
@article{arxiv.0809.2574,
title = {Elliptic Hypergeometric Laurent Biorthogonal Polynomials with a Dense Point Spectrum on the Unit Circle},
author = {Satoshi Tsujimoto and Alexei Zhedanov},
journal= {arXiv preprint arXiv:0809.2574},
year = {2009}
}