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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gasper, G. and Rahman, M. (1990). Basic Hypergeometric Series. Cambridge University Press, Cambridge.
Koelink, E. and Rosengren, H. (2002). Transmutation kernels for the little q-Jacobi function transform. Rocky Mountain J. Math., 32:703–738.
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.
Stokman, J. V. (2003). Askey-Wilson functions and quantum groups. Preprint.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/0-387-24233-3_15
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-24231-6
Online ISBN: 978-0-387-24233-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)