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Two Families of Associated Wilson Polynomials

Published online by Cambridge University Press:  20 November 2018

M. E. H. Ismail ,
J. Letessier ,
G. Valent  and
J. Wimp
M. E. H. Ismail
Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida, 33620.
J. Letessier
Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida, 33620.
G. Valent
Affiliation:
Laboratoire de Physique Théorique et Hautes Energies, Université Paris 7, Tour 24-5e étage 2 Place Jussieu, 75251 Paris Cedex 05, France
J. Wimp
Affiliation:
Department of Mathematics and Computer Science, Drexel University, Philadelphia, Pennsylvania, 19104.
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Abstract

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Two families of associated Wilson polynomials are introduced. Both families are birth and death process polynomials, satisfying the same recurrence relation but having different initial conditions. Contiguous relations for generalized hypergeometric functions of the type 7F6 are derived and used to find explicit representations for the polynomials and to compute the corresponding continued fractions. The absolutely continuous components of the orthogonality measures of both families are computed. Generating functions are also given.

Keywords

Wilson polynomialsassociated polynomialsgenerating functionshypergeometric functionsweight functionscontiguous relationsbirth and death processes33A6542C05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 4 , 01 August 1990 , pp. 659 - 695
Copyright
Copyright © Canadian Mathematical Society 1990

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