An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
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Publication:2272054
DOI10.1016/j.jmaa.2009.05.052zbMath1183.34033arXiv0807.3939OpenAlexW1974525177MaRDI QIDQ2272054
Niky Kamran, Robert Milson, Daivd Gómez-Ullate
Publication date: 5 August 2009
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0807.3939
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Cites Work
- The Sobolev orthogonality and spectral analysis of the Laguerre polynomials \(\{L_{n}^{-k}\}\) for positive integers \(k\)
- Die Charakterisierung der klassischen orthogonalen Polynome durch Sturm- Liouvillesche Differentialgleichungen
- An extension of Bochner's problem: exceptional invariant subspaces
- A generalization of a theorem of Bochner
- Orthogonality of the Jacobi polynomials with negative integer parameters
- The \(q\)-version of a theorem of Bochner
- Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
- Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
- Differential Equation for Classical-Type Orthogonal Polynomials
- The connection between systems of polynomials orthogonal with respect to different distribution functions
- Eine Bemerkung über die Charakterisierung der „klassischen” orthogonalen Polynome
- Orthogonal polynomial solutions of linear ordinary differential equations
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
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