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Associated Continuous Hahn Polynomials

Published online by Cambridge University Press:  20 November 2018

Dharma P. Gupta ,
Mourad E. H. Ismail  and
David R. Masson
Dharma P. Gupta
Affiliation:
Department of Mathematics, York University, North York, Ontario M3J 1P3
Mourad E. H. Ismail
Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida, USA 33620-5700
David R. Masson
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1A1
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Abstract

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Explicit solutions to the recurrence relation for associated continuous Hahn polynomials are derived using 3F2 contiguous relations. These solutions are used to obtain a new continued fraction and the associated absolutely continuous measure. An exceptional case is shown to yield entry 33 in Chapter 12 of Ramanujan's second notebook.

Keywords

33A65Continued fractionscontiguous relationshypergeometric functionsorthogonal polynomialsreal and complex weight functions
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 6 , 01 December 1991 , pp. 1263 - 1280
Copyright
Copyright © Canadian Mathematical Society 1991

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