The Askey scheme as a four-manifold with corners

Hypergeometric Origins of Diophantine Properties Associated with the Askey Scheme

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 ...

Annual Meeting of the Four Corners Section of the APS

Annual Meeting of the Four Corners Section of the APS

Annual Meeting of the Four Corners Section of the APS

Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme

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 valu...