Title

HYPERGEOMETRIC ORIGINS OF DIOPHANTINE PROPERTIES ASSOCIATED WITH THE ASKEY SCHEME

Authors

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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