Two limit transitions involving multivariable BC type Askey-Wilson polynomials

• Autorzy: Jasper V. Stokman
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1997
• Tom: 40
• Numer: 1
• Strony: 415-428

Daty

wydano

1997

Twórcy

autor

Jasper V. Stokman

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

Bibliografia

• [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.
• [AW] R. Askey, J. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 54 (1985), no. 319.
• [K1] T.H. Koornwinder, Askey-Wilson polynomials for root systems of type BC, Contemp. Math. 138 (1992), 189-204.
• [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.
• [M] I.G. Macdonald, Orthogonal polynomials associated with root systems, preprint 1988.
• [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.
• [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.
• [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.