Limit transitions for BC type multivariable orthogonal polynomials

Canadian Journal of Mathematics

Volumn 49, Issue 2, 1997, Pages 373-404

  Stokman, Jasper V ^a   Koornwinder, Tom H ^a  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000381085     PISSN: 0008414X     EISSN: None     Source Type: Journal    
DOI: 10.4153/CJM-1997-019-9     Document Type: Article

References (23)

1. G. E. Andrews and R. Askey, Enumeration of partitions: the role of Eulerian series and q-orthogonal polynomials. In: Higher Combinatorics, (ed. M. Aigner), Reidel, Boston, Massachusetts, 1977, 3-26.
2. _, Classical orthogonal polynomials. In: Polynômes Orthogonaux et Applications, (eds., C. Brezinski, A. Draux, A.P. Magnus, P. Maroni and A. Ronveaux), Lecture Notes in Math. 1171, Springer, New York, 1985, 36-62.
3. R. Askey, Some basic hypergeometric extensions of integrals of Selberg and Andrews, SIAM J. Math. Anal. 11(1980), 938-951.
4. R. Askey and J. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. (319) 54(1985).
5. J. F. van Diejen, Commuting difference operators with polynomial eigenfunctions, Compositio Math. 95(1995), 183-233.
6. A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions Vol. 2, McGraw-Hill, 1953.
7. R. J. Evans, Multidimensional beta and gamma integrals, Contemp. Math. 166(1994), 341-357.
8. G. Gasper and M. Rahman, Basic hypergeometric series, Encyclopedia of Mathematics and its Applications 35, Cambridge Univ. Press, 1990.
9. L. Habsieger, Une q-intégrale de Selberg et Askey, SIAM J. Math. Anal. 19(1988), 1475-1489.
10. G. J. Heckman, Root systems and hypergeometric functions II, Compositio Math. 64(1987), 353-373.
11. _, An elementary approach to the hypergeometric shift operators of Opdam, Invent. Math. 103(1991), 341-350.
12. G. J. Heckman and E. M. Opdam, Root systems and hypergeometric functions I, Compositio Math. 64(1987), 329-352.
13. K. W. J. Kadell, A proof of Askey's conjectured q-analogue of Selberg's integral and a conjecture of Morris, SIAM J. Math. Anal. 19(1988), 969-986.
14. T. H. Koornwinder, Askey-Wilson polynomials for root systems of type BC, Contemp. Math. 138(1992), 189-204.
15. _, Askey-Wilson polynomials as zonal spherical functions on the SU(2) quantum group, SIAM J. Math. Anal. 24(1993), 795-813.
16. _, Compact quantum groups and q-special functions. In: Representations of Lie groups and quantum groups, (eds., V. Baldoni and V. Baldoni and M. A. Picardello) Pitman Research Notes in Math. Series 311, Longman Scientific and Technical, 1994.
17. _, Jacobi functions as limit cases of q-ultraspherical polynomials, J. Math. Anal. Appl. 148(1990), 44-54.
18. I. G. Macdonald, Orthogonal polynomials associated with root systems, (1980), preprint.
19. _, Symmetric Functions and Hall polynomials, Oxford Univ. Press London, New York, 1979.
20. J. V. Stokman, Multivariable big and little q-Jacobi polynomials, Mathematical preprint series, Univ. of Amsterdam, 1995, report 95-16; SIAM J. Math. Anal, to appear.
21. _, Two limit transitions involving multivariable BC type Askey-Wilson polynomials, Mathematical preprint series, Univ. of Amsterdam, 1996, report 96-01; Proceedings of the Mini-Semester on Quantum Groups and Quantum Spaces, Warsaw, 1995, Banach Center Publications, to appear.
22. _, Two limit transitions involving multivariable BC type Askey-Wilson polynomials, Mathematical preprint series, Univ. of Amsterdam, 1996, report 96-01; Proceedings of the Mini-Semester on Quantum Groups and Quantum Spaces, Warsaw, 1995, Banach Center Publications, to appear.
23. L. Vretare, Formulas for elementary spherical functions and generalized Jacobi polynomials, SIAM J. Math. Anal. 15(1984), 805-833.