Continuous Hahn Functions as Clebsch-Gordan Coefficients

  • Wolter Groenevelt
  • Erik Koelink
  • Hjalmar Rosengren
Part of the Developments in Mathematics book series (DEVM, volume 13)


An explicit bilinear generating function for Meixner-Pollaczek polynomials is proved. This formula involves continuous dual Hahn polynomials, Meixner-Pollaczek functions, and non-polynomial 3 F 2-hypergeometric functions that we consider as continuous Hahn functions. An integral transform pair with continuous Hahn functions as kernels is also proved. These results have an interpretation for the tensor product decomposition of a positive and a negative discrete series representation of su(1, 1) with respect to hyperbolic bases, where the Clebsch-Gordan coefficients are continuous Hahn functions.


Tensor Product Orthogonal Polynomial Summation Formula Discrete Series Generalize Eigenvector 
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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Wolter Groenevelt
    • 1
  • Erik Koelink
    • 1
  • Hjalmar Rosengren
    • 2
  1. 1.Technische Universiteit Delft EWI-TWADelftThe Netherlands
  2. 2.Department of MathematicsChalmers University of Technology and Göteborg UniversityGöteborgSweden

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