Geodesic
$Q$-classical orthogonal polynomials: A very classical approach
Electronic transactions on numerical analysis, Tome 9 (1999), pp. 112-127.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The q - classical orthogonal polynomials defined by Hahn satisfy a Sturm-Liouville type equation in geometric differences. Working with this, we classify the q - classical polynomials in twelve families according to the zeros of the polynomial coefficients of the equation and the behavior concerning to q - 1 . We determine a q - analogue of the weight function for the twelve families, and we give a representation of its orthogonality relation and its q - 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.
Classification : 33D25
Keywords: orthogonal q, polynomials, classical polynomials 
@article{ETNA_1999__9__a3,
     author = {Marcell\'an, F. and Medem, J.C.},
     title = {$Q$-classical orthogonal polynomials: {A} very classical approach},
     journal = {Electronic transactions on numerical analysis},
     pages = {112--127},
     publisher = {mathdoc},
     volume = {9},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1999__9__a3/}
}
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Marcellán, F.; Medem, J.C. $Q$-classical orthogonal polynomials: A very classical approach. Electronic transactions on numerical analysis, Tome 9 (1999), pp. 112-127. http://geodesic.mathdoc.fr/item/ETNA_1999__9__a3/