Volume 9, pp. 112-127, 1999.
classical orthogonal polynomials: a very classical approach
F. Marcellán and J. C. Medem
Abstract
The classical orthogonal polynomials defined by Hahn satisfy
a Sturm-Liouville type equation in geometric
differences. Working with this, we classify the classical
polynomials in twelve families according to the
zeros of the polynomial coefficients of the equation and the
behavior concerning to . We determine
a analogue of the weight function for the twelve
families, and we give a representation of its
orthogonality relation and its integral. We
describe this representation in some normal and
special cases (indeterminate moment problem and finite
orthogonal sequences). Finally, the Sturm-Liouville type
equation allows us to establish the correspondence between
this classification and the Askey Scheme.
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Key words
orthogonal polynomials, classical polynomials.
AMS subject classifications
33D25.
