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A Bilateral Series Involving Basic Hypergeometric Functions

  • Hjalmar Rosengren
Chapter
Part of the Developments in Mathematics book series (DEVM, volume 13)

Abstract

We prove a summation formula for a bilateral series whose terms are products of two basic hypergeometric functions. In special cases, series of this type arise as matrix elements of quantum group representations.

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References

  1. Gasper, G. and Rahman, M. (1990). Basic Hypergeometric Series. Cambridge University Press, Cambridge.Google Scholar
  2. Koelink, E. and Rosengren, H. (2002). Transmutation kernels for the little q-Jacobi function transform. Rocky Mountain J. Math., 32:703–738.CrossRefMathSciNetGoogle Scholar
  3. Koelink, E. and Stokman, J. V. (2001). Fourier transforms on the quantum su(1, 1) group. Publ. Res. Inst. Math. Sci., 37:621–715. With an appendix by M. Rahman.MathSciNetGoogle Scholar
  4. Stokman, J. V. (2003). Askey-Wilson functions and quantum groups. Preprint.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Hjalmar Rosengren
    • 1
  1. 1.Department of MathematicsChalmers University of Technology and Göteborg UniversityGöteborgSweden

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