Academic Editor: M. Lakshmanan
Copyright © 2009 M. Bruschi et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 values of their parameters,
factorizations are identified yielding some or all of their
zeros—generally given by simple expressions in terms of
relations). The factorization findings generally are applicable
for values of the Askey polynomials that extend beyond those for
which the standard orthogonality relations hold. Most of these
results are not (yet) reported in the standard compilations.