# Two limit transitions involving multivariable BC type Askey-Wilson polynomials

Banach Center Publications (1997)

- Volume: 40, Issue: 1, page 415-428
- ISSN: 0137-6934

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topStokman, Jasper. "Two limit transitions involving multivariable BC type Askey-Wilson polynomials." Banach Center Publications 40.1 (1997): 415-428. <http://eudml.org/doc/252213>.

@article{Stokman1997,

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.},

author = {Stokman, Jasper},

journal = {Banach Center Publications},

keywords = {multivariable orthogonal polynomials; BC type Askey-Wilson polynomials; second order q-difference operators; BC type big and little q-Jacobi polynomials},

language = {eng},

number = {1},

pages = {415-428},

title = {Two limit transitions involving multivariable BC type Askey-Wilson polynomials},

url = {http://eudml.org/doc/252213},

volume = {40},

year = {1997},

}

TY - JOUR

AU - Stokman, Jasper

TI - Two limit transitions involving multivariable BC type Askey-Wilson polynomials

JO - Banach Center Publications

PY - 1997

VL - 40

IS - 1

SP - 415

EP - 428

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/252213

ER -

## References

top- [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. Zbl0572.33012
- [K1] T.H. Koornwinder, Askey-Wilson polynomials for root systems of type BC, Contemp. Math. 138 (1992), 189-204. Zbl0797.33014
- [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. Zbl0799.33015
- [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.

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