Additional recursion relations, factorizations, and diophantine properties associated with the polynomials of the Askey scheme (Articolo in rivista)

Type
Label
  • Additional recursion relations, factorizations, and diophantine properties associated with the polynomials of the Askey scheme (Articolo in rivista) (literal)
Anno
  • 2009-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1155/2009/268134 (literal)
Alternative label
  • Bruschi M.; Calogero F.; Droghei R. (2009)
    Additional recursion relations, factorizations, and diophantine properties associated with the polynomials of the Askey scheme
    in Advances in Mathematical Physics (Online)
    (literal)
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  • Bruschi M.; Calogero F.; Droghei R. (literal)
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  • http://www.scopus.com/inward/record.url?eid=2-s2.0-72449211981&partnerID=q2rCbXpz (literal)
Rivista
Note
  • Scopu (literal)
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  • Dipartimento di Fisica, Università di Roma La Sapienza, 00185 Roma, Italy; Istituto Nazionale di Fisica Nucleare, Sezione di Roma, 00185 Roma, Italy; Dipartimento di Fisica, Università Roma Tre, 00146 Roma, Italy (literal)
Titolo
  • Additional recursion relations, factorizations, and diophantine properties associated with the polynomials of the Askey scheme (literal)
Abstract
  • 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. Copyright © 2009 M. Bruschi et al. (literal)
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