2009/03/10 by Yang Chen, Mourad E. H. Ismail, Chen, Yang +1
Mathematics · #33C20 #33C45 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:33C20 #msc:33C45
paper · pdf · doi:10.48550/arxiv.0903.1722
10 pages
arxiv created 2009/03/10 · arxiv updated 2009/12/01
The "Diophantine" property of the zeros of certain polynomials in the Askey scheme, recently discovered by Calogero and his collaborators, is 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-analogue of the summation theorems, zeros of these polynomials explicitly, which are no longer integer valued. This goes beyond the results obtained by the Authors mentioned above.