HYPERGEOMETRIC ORIGINS OF DIOPHANTINE PROPERTIES ASSOCIATED WITH THE ASKEY SCHEME

    Authors

    Y. Chen;M. E. H. Ismail

    Comments

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    Abbreviated Journal Title

    Proc. Amer. Math. Soc.

    Keywords

    Generalized hypergeometric series; basic hypergeometric series; summation theorems; ORTHOGONAL POLYNOMIALS; TRIDIAGONAL MATRICES; Mathematics, Applied; Mathematics

    Abstract

    The "Diophantine" properties of the zeros of certain polynomials in the Askey scheme, recently discovered by Calogero and his collaborators, are explained, with suitably chosen parameter values, in terms of the summation theorem of hypergeometric series. Here the Diophantine property refers to integer valued zeros. It turns out that the same procedure can also be applied to polynomials arising from I lie basic hypergeometric series. We found, with suitably chosen parameters and certain q-analogues of the summation theorems. zeros of these polynomials explicitly which are no longer integer valued. This goes beyond the results obtained by the authors previously mentioned.

    Journal Title

    Proceedings of the American Mathematical Society

    Volume

    138

    Issue/Number

    3

    Publication Date

    1-1-2010

    Document Type

    Article

    Language

    English

    First Page

    943

    Last Page

    951

    WOS Identifier

    WOS:000275015700019

    ISSN

    0002-9939

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