A ] 2 4 M ay 1 99 4 Q - Hermite Polynomials and Classical Orthogonal Polynomials
نویسنده
چکیده
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 Szegő 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. Running title: Classical Orthogonal Polynomials. 1990 Mathematics Subject Classification: Primary 33D45, Secondary . em
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