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Volume 18 of the series The IMA Volumes in Mathematics and Its Applications pp 151158
Continuous qHermite Polynomials When q > 1
 Richard AskeyAffiliated withDepartment of Mathematics, University of WisconsinMadison
Abstract
The continuous qHermite polynomials have a reasonably well known orthogonality relation when — 1 < q < 1. When q > 1 the change of variables x → ix lends to a set of orthogonal polynomials. The same happens for the continuous qultraspherical polynomials, but now only finitely many polynomials are orthogonal with respect to a positive measure. A positive measure is found in each of these cases.
 Title
 Continuous qHermite Polynomials When q > 1
 Book Title
 qSeries and Partitions
 Pages
 pp 151158
 Copyright
 1989
 DOI
 10.1007/9781468406375_12
 Print ISBN
 9781468406399
 Online ISBN
 9781468406375
 Series Title
 The IMA Volumes in Mathematics and Its Applications
 Series Volume
 18
 Series ISSN
 09406573
 Publisher
 Springer US
 Copyright Holder
 SpringerVerlag New York Inc.
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 Industry Sectors
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 Editors

 Dennis Stanton ^{(1)}
 Editor Affiliations

 1. School of Mathematics, University of Minnesota
 Authors

 Richard Askey ^{(2)}
 Author Affiliations

 2. Department of Mathematics, University of WisconsinMadison, Madison, Wisconsin, 53706, USA
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