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Some Systems of Multivariable Orthogonal Askey-Wilson Polynomials

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Theory and Applications of Special Functions

Part of the book series: Developments in Mathematics ((DEVM,volume 13))

Abstract

In 1991 Tratnik derived two systems of multivariable orthogonal Wilson polynomials and considered their limit cases. q-Analogues of these systems are derived, yielding systems of multivariable orthogonal Askey-Wilson polynomials and their special and limit cases.

Supported, in part, by an NSERC grant #A6197.

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References

  • Askey, R. and Wilson, J. A. (1979). A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols. SIAM J. Math. Anal., 10:1008–1016.

    Article  MathSciNet  Google Scholar 

  • Askey, R. and Wilson, J. A. (1985). Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Memoirs Amer. Math. Soc., 319.

    Google Scholar 

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

    Google Scholar 

  • Gasper, G. and Rahman, M. (2003). q-analogues of some multivariable biorthogonal polynomials. This Proceedings.

    Google Scholar 

  • Koekoek, R. and Swarttouw, R. F. (1998). The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue. Report 98–17, Delft University of Technology.

    Google Scholar 

  • Koelink, H. T. and Van der Jeugt, J. (1998). Convolutions for orthogonal polynomials from Lie and quantum algebra representations. SIAM J. Math. Anal., 29:794–822.

    Article  MathSciNet  Google Scholar 

  • Koornwinder, T. H. (1992). Askey-Wilson polynomials for root systems of type BC. In Hypergeometric functions on domains of positivity, Jack polynomials, and applications (Tampa, FL, 1991), volume 138 of Contemp. Math., pages 189–204. Amer. Math. Soc., Providence, RI.

    Google Scholar 

  • Stokman, J. V. (1999). On BC type basic hypergeometric orthogonal polynomials. Trans. Amer. Math. Soc., 352:1527–1579.

    Article  MathSciNet  Google Scholar 

  • Tratnik, M. V. (1989). Multivariable Wilson polynomials. J. Math. Phys., 30:2001–2011.

    Article  MATH  MathSciNet  Google Scholar 

  • Tratnik, M. V. (1991a). Some multivariable orthogonal polynomials of the Askey tableau—continuous families. J. Math. Phys., 32:2065–2073.

    Article  MATH  MathSciNet  Google Scholar 

  • Tratnik, M. V. (1991b). Some multivariable orthogonal polynomials of the Askey tableau—discrete families. J. Math. Phys., 32:2337–2342.

    Article  MATH  MathSciNet  Google Scholar 

  • Wilson, J. A. (1980). Some hypergeometric orthogonal polynomials. SIAM J. Math. Anal., 11:690–701.

    Article  MATH  MathSciNet  Google Scholar 

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Gasper, G., Rahman, M. (2005). Some Systems of Multivariable Orthogonal Askey-Wilson Polynomials. 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_10

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