Continuous q-Hermite Polynomials When q > 1

  • Richard Askey
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 18)

Abstract

The continuous q-Hermite polynomials have a reasonably well known orthogonality relation when — 1 < q < 1. When q > 1 the change of variables xix lends to a set of orthogonal polynomials. The same happens for the continuous q-ultraspherical 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.

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Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Richard Askey
    • 1
  1. 1.Department of MathematicsUniversity of Wisconsin-MadisonMadisonUSA

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