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.
@article{bwmeta1.element.bwnjournal-article-bcpv40z1p415bwm, author = {Stokman, Jasper}, title = {Two limit transitions involving multivariable BC type Askey-Wilson polynomials}, journal = {Banach Center Publications}, volume = {38}, year = {1997}, pages = {415-428}, zbl = {0874.33013}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv40z1p415bwm} }
Stokman, Jasper. Two limit transitions involving multivariable BC type Askey-Wilson polynomials. Banach Center Publications, Tome 38 (1997) pp. 415-428. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv40z1p415bwm/
[000] [AA] G.E. Andrews, R. Askey, Classical orthogonal polynomials, in: Polynômes Orthogonaux et Applications, C. Brezinski, A. Draux, A.P. Magnus, P. Maroni and A. Ronveaux, eds., Lecture Notes in Math. 1171, Springer, New York, 1985, 36-62.
[001] [AW] R. Askey, J. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 54 (1985), no. 319. | Zbl 0572.33012
[002] [K1] T.H. Koornwinder, Askey-Wilson polynomials for root systems of type BC, Contemp. Math. 138 (1992), 189-204. | Zbl 0797.33014
[003] [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. | Zbl 0799.33015
[004] [M] I.G. Macdonald, Orthogonal polynomials associated with root systems, preprint 1988.
[005] [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.
[006] [S1] J.V. Stokman, Askey-Wilson polynomials with partly discrete ortogonality measure, Mathematical preprint series, Univ. of Amsterdam (1996), report 96-06, to appear in the Ramanujan Journal.
[007] [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.