Title

Hypergeometric Origins Of Diophantine Properties Associated With The Askey Scheme

Keywords

Basic hypergeometric series; Generalized hypergeometric series; Summation theorems

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 the 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. © 2009 American Mathematical Society.

Publication Date

3-1-2010

Publication Title

Proceedings of the American Mathematical Society

Volume

138

Issue

3

Number of Pages

943-951

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/S0002-9939-09-10106-5

Socpus ID

73949087563 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/73949087563

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