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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Veröffentlicht in:Symmetry, integrability and geometry, methods and applications Jg. 5; S. 033
1. Verfasser: Tsujimoto, Satoshi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Kiev National Academy of Sciences of Ukraine 01.01.2009
National Academy of Science of Ukraine
Schlagworte:
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
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Abstract 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.
AbstractList 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.
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 {}_3E_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.
Author Tsujimoto, Satoshi
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Snippet Using the technique of the elliptic Frobenius determinant, we construct new elliptic solutions of the QD-algorithm. These solutions can be interpreted as...
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StartPage 033
SubjectTerms 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
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