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  • 标题:Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme
  • 本地全文:下载
  • 作者:M. Bruschi ; F. Calogero ; R. Droghei
  • 期刊名称:Advances in Mathematical Physics
  • 印刷版ISSN:1687-9120
  • 电子版ISSN:1687-9139
  • 出版年度:2009
  • 卷号:2009
  • DOI:10.1155/2009/268134
  • 出版社:Hindawi Publishing Corporation
  • 摘要: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.
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