Elliptic Hypergeometric Laurent Biorthogonal Polynomials with a Dense Point Spectrum on the Unit Circle

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 ter...

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Bibliographic Details
Published in:	Symmetry, integrability and geometry, methods and applications Vol. 5; p. 033
Main Author:	Tsujimoto, Satoshi
Format:	Journal Article
Language:	English
Published:	Kiev National Academy of Sciences of Ukraine 01.01.2009 National Academy of Science of Ukraine
Subjects:	dense point spectrum elliptic Frobenius determinant elliptic hypergeometric functions Krall-Jacobi orthogonal polynomials orthogonal and biorthogonal polynomials on the unit circle QD-algorithm quadratic operator pencils
ISSN:	1815-0659, 1815-0659
Online Access:	Get full text
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Summary:	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 3E2(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.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1815-0659 1815-0659
DOI:	10.3842/SIGMA.2009.033