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Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme
Joint Authors
Droghei, R.
Bruschi, M.
Calogero, F.
Source
Advances in Mathematical Physics
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-43, 43 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-04-02
Country of Publication
Egypt
No. of Pages
43
Main Subjects
Abstract EN
In this paper, we apply to (almost) all the “named” polynomials of the Askey scheme, as defined by their standard three-term recursion relations, the machinery developed in previous papers.
For each of these polynomials we identify at least one additional recursion relation involving a shift in some of the parameters they feature, and for several of these polynomials characterized by special values of their parameters, factorizations are identified yielding some or all of their zeros—generally given by simple expressions in terms of integers (Diophantine relations).
The factorization findings generally are applicable for values of the Askey polynomials that extend beyond those for which the standard orthogonality relations hold.
Most of these results are not (yet) reported in the standard compilations.
American Psychological Association (APA)
Bruschi, M.& Calogero, F.& Droghei, R.. 2009. Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme. Advances in Mathematical Physics،Vol. 2009, no. 2009, pp.1-43.
https://search.emarefa.net/detail/BIM-458897
Modern Language Association (MLA)
Bruschi, M.…[et al.]. Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme. Advances in Mathematical Physics No. 2009 (2009), pp.1-43.
https://search.emarefa.net/detail/BIM-458897
American Medical Association (AMA)
Bruschi, M.& Calogero, F.& Droghei, R.. Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme. Advances in Mathematical Physics. 2009. Vol. 2009, no. 2009, pp.1-43.
https://search.emarefa.net/detail/BIM-458897
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-458897