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Complex Weight Functions for Classical Orthogonal Polynomials

Published online by Cambridge University Press:  20 November 2018

Mourad E. H. Ismail ,
David R. Masson  and
Mizan Rahman
Mourad E. H. Ismail
Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida 33620, U. S. A.
David R. Masson
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1A1
Mizan Rahman
Affiliation:
Department of Mathematics, Carleton University, Ottawa, Ontario K1S 1B6
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Abstract

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We give complex weight functions with respect to which the Jacobi, Laguerre, little q-Jacobi and Askey-Wilson polynomials are orthogonal. The complex functions obtained are weight functions in a wider range of parameters than the real weight functions. They also provide an alternative to the recent distributional weight functions of Morton and Krall, and the more recent hyperfunction weight functions of Kim.

Keywords

33A6533A3042C05Complex weight functionsreal weight functionsJacobiLaguerrelittle q-JacobiAskey-Wilson polynomialsdistributional weight functionshyperfunction weight functionsthree term recurrence relationsinner products.
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 6 , 01 December 1991 , pp. 1294 - 1308
Copyright
Copyright © Canadian Mathematical Society 1991

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