Elliptic Hypergeometric Laurent Biorthogonal Polynomials with a Dense Point Spectrum on the Unit Circle
| dc.creator | Tsujimoto, Satoshi | |
| dc.creator | Zhedanov, Alexei | |
| dc.date | 2008-09-15 | |
| dc.date | 2009-03-19 | |
| dc.date.accessioned | 2026-07-07T12:53:25Z | |
| dc.date.available | 2026-07-07T12:53:25Z | |
| dc.description | Using the technique of the elliptic Frobenius determinant, we construct new elliptic solutions of the $QD$-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 ${_3}E_2(z)$. 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. | |
| dc.identifier | https://arxiv.org/abs/0809.2574 | |
| dc.identifier | http://arxiv.org/abs/0809.2574 | |
| dc.identifier | SIGMA 5 (2009), 033, 30 pages | |
| dc.identifier | doi:10.3842/SIGMA.2009.033 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223615 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | 33E05, 33E30, 33C47 | |
| dc.title | Elliptic Hypergeometric Laurent Biorthogonal Polynomials with a Dense Point Spectrum on the Unit Circle | |
| dc.type | text |