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ArticleOriginal scientific text

Title

Two limit transitions involving multivariable BC type Askey-Wilson polynomials

Authors 1

Affiliations

  1. Department of Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands

Abstract

In the first part (without proofs) an orthogonality measure with partly discrete and partly continuous support will be introduced for the five parameter family of multivariable BC type Askey-Wilson polynomials. In the second part, the limit transitions from BC type Askey-Wilson polynomials to BC type big and little q-Jacobi polynomials will be described in detail.

Keywords

ENG
multivariable orthogonal polynomials, BC type Askey-Wilson polynomials, second order q-difference operators, BC type big and little q-Jacobi polynomials

Bibliography

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  2. [AW] R. Askey, J. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 54 (1985), no. 319.
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  4. [K2] T.H. Koornwinder, Askey-Wilson polynomials as zonal spherical functions on the SU(2) quantum group, SIAM J. Math. Anal. 24 (1993), pp. 795-813.
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  6. [S] J.V. Stokman, Multivariable big and little q-Jacobi polynomials, Mathematical preprint series, Univ. of Amsterdam (1995), report 95-16, to appear in SIAM J. Math. Anal.
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  8. [SK] J.V. Stokman, T.H. Koornwinder, Limit transitions for BC type multivariable orthogonal polynomials, Mathematical preprint series, Univ. of Amsterdam (1995), report 95-19. To appear in Canad. J. Math.
Banach Center Publications
1997/40/1
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Pages:
415-428
Main language of publication
English
Published
1997
Exact and natural sciences