q-Hermite Polynomials and Classical Orthogonal Polynomials

Berg, Christian ; Ismail, Mourad E. H.

Canadian journal of mathematics, Tome 48 (1996) no. 1, pp. 43-63

Résumé

We use generating functions to express orthogonality relations in the form of q-beta. integrals. The integrand of such a q-beta. integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials of Szegö and leads naturally to the Al-Salam-Chihara polynomials then to the Askey-Wilson polynomials, the big q-Jacobi polynomials and the biorthogonal rational functions of Al-Salam and Verma, and some recent biorthogonal functions of Al-Salam and Ismail.

Détail

DOI : 10.4153/CJM-1996-002-4

Mots-clés : 33D45, 33A65, 44A60, Askey-Wilson polynomials, q-orthogonal polynomials, orthogonality relations, q-beta integrals, q-Hermite polynomials, biorthogonal rational functions

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