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A Bilateral Series Involving Basic Hypergeometric Functions

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Book cover Theory and Applications of Special Functions

Part of the book series: Developments in Mathematics ((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

  • Gasper, G. and Rahman, M. (1990). Basic Hypergeometric Series. Cambridge University Press, Cambridge.

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  • Koelink, E. and Rosengren, H. (2002). Transmutation kernels for the little q-Jacobi function transform. Rocky Mountain J. Math., 32:703–738.

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  • 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.

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  • Stokman, J. V. (2003). Askey-Wilson functions and quantum groups. Preprint.

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© 2005 Springer Science+Business Media, Inc.

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Rosengren, H. (2005). A Bilateral Series Involving Basic Hypergeometric Functions. In: Ismail, M.E., Koelink, E. (eds) Theory and Applications of Special Functions. Developments in Mathematics, vol 13. Springer, Boston, MA. https://doi.org/10.1007/0-387-24233-3_15

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