Diophantine properties of orthogonal polynomials and rational functions Article Swipe
Mourad E. H. Ismail
,
Mizan Rahman
·
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.1090/proc/12355
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.1090/proc/12355
Calogero and his collaborators recently observed that some hypergeometric polynomials can be factored as a product of two polynomials, one of which is factored into a product of linear terms. Chen and Ismail showed that this property prevails through all polynomials in the Askey scheme. We show that this factorization property is also shared by the associated Wilson and Askey-Wilson polynomials and some biorthogonal rational functions. This is applied to a specific model of an isochronous system of particles with small oscillations around the equilibrium position.
Related Topics
Concepts
Orthogonal polynomials
Mathematics
Classical orthogonal polynomials
Pure mathematics
Hahn polynomials
Biorthogonal system
Discrete orthogonal polynomials
Product (mathematics)
Wilson polynomials
Chebyshev polynomials
Property (philosophy)
Askey–Wilson polynomials
Diophantine equation
Unique factorization domain
Jacobi polynomials
Rational function
Gegenbauer polynomials
Factorization
Mathematical analysis
Computer science
Epistemology
Wavelet
Philosophy
Wavelet transform
Artificial intelligence
Geometry
Algorithm
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1090/proc/12355
- OA Status
- green
- Cited By
- 5
- References
- 20
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2589360734
All OpenAlex metadata
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https://openalex.org/W2589360734Canonical identifier for this work in OpenAlex
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https://doi.org/10.1090/proc/12355Digital Object Identifier
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Diophantine properties of orthogonal polynomials and rational functionsWork title
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articleOpenAlex work type
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enPrimary language
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2017Year of publication
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2017-02-20Full publication date if available
- Authors
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Mourad E. H. Ismail, Mizan RahmanList of authors in order
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https://doi.org/10.1090/proc/12355Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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- Concepts
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Orthogonal polynomials, Mathematics, Classical orthogonal polynomials, Pure mathematics, Hahn polynomials, Biorthogonal system, Discrete orthogonal polynomials, Product (mathematics), Wilson polynomials, Chebyshev polynomials, Property (philosophy), Askey–Wilson polynomials, Diophantine equation, Unique factorization domain, Jacobi polynomials, Rational function, Gegenbauer polynomials, Factorization, Mathematical analysis, Computer science, Epistemology, Wavelet, Philosophy, Wavelet transform, Artificial intelligence, Geometry, AlgorithmTop concepts (fields/topics) attached by OpenAlex
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5Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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