Koornwinder, Tom H. Erratum to: “Charting the \(q\)-Askey scheme. II: The \(q\)-Zhedanov scheme”. (English) Zbl 07754821 Indag. Math., New Ser. 34, No. 6, 1419-1420 (2023). MSC: 33C05 33C45 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Indag. Math., New Ser. 34, No. 6, 1419--1420 (2023; Zbl 07754821) Full Text: DOI
Koornwinder, Tom H. Dual addition formulas: the case of continuous \(q\)-ultraspherical and \(q\)-Hermite polynomials. (English) Zbl 07695113 Ramanujan J. 61, No. 2, 425-444 (2023). MSC: 33D45 39B12 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Ramanujan J. 61, No. 2, 425--444 (2023; Zbl 07695113) Full Text: DOI arXiv
Koornwinder, Tom H. Charting the \(q\)-Askey scheme. II. The \(q\)-Zhedanov scheme. (English) Zbl 07654705 Indag. Math., New Ser. 34, No. 2, 317-337 (2023); erratum ibid. 34, No. 6, 1419-1420 (2023). MSC: 33D45 33C05 33C45 33C80 33D80 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Indag. Math., New Ser. 34, No. 2, 317--337 (2023; Zbl 07654705) Full Text: DOI arXiv
Koornwinder, Tom H. Charting the \(q\)-Askey scheme. III. Verde-Star scheme for \(q=1\). arXiv:2307.06668 Preprint, arXiv:2307.06668 [math.CA] (2023). MSC: 33C45 BibTeX Cite \textit{T. H. Koornwinder}, ``Charting the $q$-Askey scheme. III. Verde-Star scheme for $q=1$'', Preprint, arXiv:2307.06668 [math.CA] (2023) Full Text: arXiv OA License
Koornwinder, Tom H. Charting the \(q\)-Askey scheme. (English) Zbl 1500.33007 Koelink, Erik (ed.) et al., Hypergeometry, integrability and Lie theory. Virtual conference, Lorentz Center, Leiden, the Netherlands, December 7–11, 2020. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 780, 79-94 (2022). MSC: 33D45 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Contemp. Math. 780, 79--94 (2022; Zbl 1500.33007) Full Text: DOI arXiv
Koornwinder, Tom H. A short survey of duality in special functions. arXiv:2102.12131 Preprint, arXiv:2102.12131 [math.CA] (2021). MSC: 33C45 33-XX BibTeX Cite \textit{T. H. Koornwinder}, ``A short survey of duality in special functions'', Preprint, arXiv:2102.12131 [math.CA] (2021) Full Text: arXiv OA License
Butzer, Paul L.; Koornwinder, Tom H. Josef Meixner: his life and his orthogonal polynomials. (English) Zbl 1405.33010 Indag. Math., New Ser. 30, No. 1, 250-264 (2019). Reviewer: Marcel G. de Bruin (Heemstede) MSC: 33C45 33D45 42C05 33C47 01A60 PDFBibTeX XMLCite \textit{P. L. Butzer} and \textit{T. H. Koornwinder}, Indag. Math., New Ser. 30, No. 1, 250--264 (2019; Zbl 1405.33010) Full Text: DOI arXiv
Koornwinder, Tom H. Dual addition formulas associated with dual product formulas. (English) Zbl 1411.33010 Nashed, M. Zuhair (ed.) et al., Frontiers in orthogonal polynomials and \(q\)-series. Papers based on the international conference, University of Central Florida, Orlando, FL, USA, May 10–12, 2015. Dedicated to Professor Mourad Ismail on his 70th birthday. Hackensack, NJ: World Scientific. Contemp. Math. Appl., Monogr. Expo. Lect. Notes 1, 373-392 (2018). MSC: 33C45 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Contemp. Math. Appl., Monogr. Expo. Lect. Notes 1, 373--392 (2018; Zbl 1411.33010) Full Text: DOI arXiv
Koornwinder, Tom H. Quadratic transformations for orthogonal polynomials in one and two variables. (English) Zbl 1409.33007 Konno, Hitoshi (ed.) et al., Representation theory, special functions and Painvlevé equations – RIMS 2015. Proceedings of the international conference on the occasion of Masatoshi Noumi’s 60th birthday, RIMS, Kyoto, Japan, March 3–6, 2015. Tokyo: Mathematical Society of Japan (MSJ). Adv. Stud. Pure Math. 76, 419-447 (2018). MSC: 33C45 33C52 33D45 33D52 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Adv. Stud. Pure Math. 76, 419--447 (2018; Zbl 1409.33007) Full Text: DOI arXiv Euclid
Koornwinder, Tom H.; Mazzocco, Marta Dualities in the \(q\)-Askey scheme and degenerate DAHA. (English) Zbl 1408.33032 Stud. Appl. Math. 141, No. 4, 424-473 (2018). MSC: 33D45 20C08 PDFBibTeX XMLCite \textit{T. H. Koornwinder} and \textit{M. Mazzocco}, Stud. Appl. Math. 141, No. 4, 424--473 (2018; Zbl 1408.33032) Full Text: DOI arXiv
Koornwinder, Tom; Kostenko, Aleksey; Teschl, Gerald Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operator. (English) Zbl 1405.33012 Adv. Math. 333, 796-821 (2018). Reviewer: Nicolae Cotfas (Bucureşti) MSC: 33C45 47B36 81U30 81Q05 PDFBibTeX XMLCite \textit{T. Koornwinder} et al., Adv. Math. 333, 796--821 (2018; Zbl 1405.33012) Full Text: DOI arXiv
Koornwinder, Tom H. Representations of SU(2) and Jacobi polynomials. arXiv:1606.08189 Preprint, arXiv:1606.08189 [math.CA] (2016). MSC: 33C45 33C80 33-01 22E45 22-01 33-03 01A60 BibTeX Cite \textit{T. H. Koornwinder}, ``Representations of SU(2) and Jacobi polynomials'', Preprint, arXiv:1606.08189 [math.CA] (2016) Full Text: arXiv OA License
Koornwinder, Tom H. Okounkov’s BC-type interpolation Macdonald polynomials and their \(q=1\) limit. (English) Zbl 1331.33038 Sémin. Lothar. Comb. 72(2014-2015), B72a, 27 p. (2015). MSC: 33D52 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Sémin. Lothar. Comb. 72, B72a, 27 p. (2015; Zbl 1331.33038) Full Text: arXiv EMIS
Koornwinder, Tom H.; Sauter, Stefan A. The intersection of bivariate orthogonal polynomials on triangle patches. (English) Zbl 1309.65145 Math. Comput. 84, No. 294, 1795-1812 (2015). MSC: 65N50 33C50 65N15 65N30 33C45 PDFBibTeX XMLCite \textit{T. H. Koornwinder} and \textit{S. A. Sauter}, Math. Comput. 84, No. 294, 1795--1812 (2015; Zbl 1309.65145) Full Text: DOI arXiv
Cagliero, Leandro; Koornwinder, Tom H. Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials. (English) Zbl 1318.33013 J. Approx. Theory 193, 20-38 (2015). Reviewer: Małgorzata Michalska (Lublin) MSC: 33C45 15A29 15B05 PDFBibTeX XMLCite \textit{L. Cagliero} and \textit{T. H. Koornwinder}, J. Approx. Theory 193, 20--38 (2015; Zbl 1318.33013) Full Text: DOI arXiv
Koornwinder, Tom H. Additions to the formula lists in ”Hypergeometric orthogonal polynomials and their \(q\)-analogues” by Koekoek, Lesky and Swarttouw. arXiv:1401.0815 Preprint, arXiv:1401.0815 [math.CA] (2014). MSC: 33C45 33D45 BibTeX Cite \textit{T. H. Koornwinder}, ``Additions to the formula lists in "Hypergeometric orthogonal polynomials and their $q$-analogues" by Koekoek, Lesky and Swarttouw'', Preprint, arXiv:1401.0815 [math.CA] (2014) Full Text: arXiv OA License
Koornwinder, Tom H. Orthogonal polynomials. (English) Zbl 1311.33007 Schneider, Carsten (ed.) et al., Computer algebra in quantum field theory. Integration, summation and special functions. Wien: Springer (ISBN 978-3-7091-1615-9/hbk; 978-1-4614-8523-0/ebook). Texts and Monographs in Symbolic Computation, 145-170 (2013). MSC: 33C45 33C47 42C05 33F10 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, in: Computer algebra in quantum field theory. Integration, summation and special functions. Wien: Springer. 145--170 (2013; Zbl 1311.33007) Full Text: DOI arXiv Link
Rösler, Margit; Koornwinder, Tom; Voit, Michael Limit transition between hypergeometric functions of type BC and type A. (English) Zbl 1405.33019 Compos. Math. 149, No. 8, 1381-1400 (2013). MSC: 33C52 43A90 33C80 53C35 33C67 PDFBibTeX XMLCite \textit{M. Rösler} et al., Compos. Math. 149, No. 8, 1381--1400 (2013; Zbl 1405.33019) Full Text: DOI arXiv
Koornwinder, Tom H.; Schlosser, Michael J. On an identity by Chaundy and Bullard. II: More history. (English) Zbl 1282.33008 Indag. Math., New Ser. 24, No. 1, 174-180 (2013). MSC: 33C05 33C45 05A19 PDFBibTeX XMLCite \textit{T. H. Koornwinder} and \textit{M. J. Schlosser}, Indag. Math., New Ser. 24, No. 1, 174--180 (2013; Zbl 1282.33008) Full Text: DOI arXiv
Diekema, Enno; Koornwinder, Tom H. Differentiation by integration using orthogonal polynomials, a survey. (English) Zbl 1259.65050 J. Approx. Theory 164, No. 5, 637-667 (2012). Reviewer: Ioana Tascu (Baia Mare) MSC: 65D25 42C05 42C40 65T60 65D10 PDFBibTeX XMLCite \textit{E. Diekema} and \textit{T. H. Koornwinder}, J. Approx. Theory 164, No. 5, 637--667 (2012; Zbl 1259.65050) Full Text: DOI arXiv
Diekema, Enno; Koornwinder, Tom H. Generalizations of an integral for Legendre polynomials by Persson and Strang. (English) Zbl 1237.33005 J. Math. Anal. Appl. 388, No. 1, 125-135 (2012). Reviewer: Alicia Cachafeiro López (Vigo) MSC: 33C45 42C05 33C47 33C05 PDFBibTeX XMLCite \textit{E. Diekema} and \textit{T. H. Koornwinder}, J. Math. Anal. Appl. 388, No. 1, 125--135 (2012; Zbl 1237.33005) Full Text: DOI arXiv
Koornwinder, Tom H. On the limit from \(q\)-Racah polynomials to big \(q\)-Jacobi polynomials. (English) Zbl 1218.33018 SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 040, 8 p. (2011). MSC: 33D45 33C45 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 040, 8 p. (2011; Zbl 1218.33018) Full Text: DOI arXiv EuDML
Koornwinder, Tom H.; Bouzeffour, Fethi Nonsymmetric Askey-Wilson polynomials as vector-valued polynomials. (English) Zbl 1216.33040 Appl. Anal. 90, No. 3-4, 731-746 (2011). MSC: 33D45 33D52 33C45 PDFBibTeX XMLCite \textit{T. H. Koornwinder} and \textit{F. Bouzeffour}, Appl. Anal. 90, No. 3--4, 731--746 (2011; Zbl 1216.33040) Full Text: DOI arXiv
Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F. [Koornwinder, Tom H.] Hypergeometric orthogonal polynomials and their \(q\)-analogues. With a foreword by Tom H. Koornwinder. (English) Zbl 1200.33012 Springer Monographs in Mathematics. Berlin: Springer (ISBN 978-3-642-05013-8/hbk; 978-3-642-26351-4/pbk; 978-3-642-05014-5/ebook). xix, 578 p. (2010). Reviewer: Anatoly Filip Grishin (Khar’kov) MSC: 33C45 33D45 PDFBibTeX XMLCite \textit{R. Koekoek} et al., Hypergeometric orthogonal polynomials and their \(q\)-analogues. With a foreword by Tom H. Koornwinder. Berlin: Springer (2010; Zbl 1200.33012) Full Text: DOI
Koornwinder, Tom H. The Askey scheme as a four-manifold with corners. (English) Zbl 1195.33053 Ramanujan J. 20, No. 3, 409-439 (2009). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33C45 33D45 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Ramanujan J. 20, No. 3, 409--439 (2009; Zbl 1195.33053) Full Text: DOI arXiv
Atakishiyeva, Mesuma K.; Atakishiyev, Natig M.; Koornwinder, Tom H. \(q\)-extension of Mehta’s eigenvectors of the finite Fourier transform for \(q\), a root of unity. (English) Zbl 1183.33035 J. Phys. A, Math. Theor. 42, No. 45, Article ID 454004, 9 p. (2009). Reviewer: Chrysoula G. Kokologiannaki (Patras) MSC: 33D45 42A38 PDFBibTeX XMLCite \textit{M. K. Atakishiyeva} et al., J. Phys. A, Math. Theor. 42, No. 45, Article ID 454004, 9 p. (2009; Zbl 1183.33035) Full Text: DOI arXiv
Koornwinder, Tom H. The relationship between Zhedanov’s algebra \(AW(3)\) and the double affine Hecke algebra in the rank one case. (English) Zbl 1134.33321 SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 063, 15 p. (2007). MSC: 33D80 33D45 17B37 20C08 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 063, 15 p. (2007; Zbl 1134.33321) Full Text: DOI arXiv EuDML EMIS
Koornwinder, Tom H. The structure relation for Askey-Wilson polynomials. (English) Zbl 1120.33018 J. Comput. Appl. Math. 207, No. 2, 214-226 (2007). Reviewer: P. R. Parthasarathy (Karlsruhe) MSC: 33D45 33C45 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, J. Comput. Appl. Math. 207, No. 2, 214--226 (2007; Zbl 1120.33018) Full Text: DOI arXiv
Koornwinder, Tom H.; Onn, Uri LU factorizations, \(q = 0\) limits, and \(p\)-adic interpretations of some \(q\)-hypergeometric orthogonal polynomials. (English) Zbl 1120.33019 Ramanujan J. 13, No. 1-3, 365-387 (2007). Reviewer: Youssef Ben Cheikh (Monastir) MSC: 33D45 33D80 PDFBibTeX XMLCite \textit{T. H. Koornwinder} and \textit{U. Onn}, Ramanujan J. 13, No. 1--3, 365--387 (2007; Zbl 1120.33019) Full Text: DOI arXiv
Koornwinder, Tom H. Lowering and raising operators for some special orthogonal polynomials. (English) Zbl 1132.33315 Kuznetsov, Vadim B. (ed.) et al., Jack, Hall-Littlewood and Macdonald polynomials. Workshop on Jack, Hall-Littlewood and Macdonald polynomials, ICMS, Edinburgh, UK, September 23–26, 2003. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3683-8/pbk). Contemporary Mathematics 417, 227-238 (2006). MSC: 33C45 33D45 33C52 05E35 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Contemp. Math. 417, 227--238 (2006; Zbl 1132.33315) Full Text: arXiv
Koornwinder, Tom H. A second addition formula for continuous \(q\)-ultraspherical polynomials. (English) Zbl 1219.33025 Ismail, Mourad E. H. (ed.) et al., Theory and applications of special functions. A volume dedicated to Mizan Rahman. Papers from the special session of the American Mathematical Society annual meeting held in Baltimore, MD, USA, January 15–18, 2003. New York, NY: Springer (ISBN 0-387-24231-7). Developments in Mathematics 13, 339-360 (2005). MSC: 33D45 33D80 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Dev. Math. 13, 339--360 (2005; Zbl 1219.33025) Full Text: DOI arXiv
Askey, R. A. (ed.); Koepf, W. (ed.); Koornwinder, T. H. (ed.) Special issue: Orthogonal polynomials and computer algebra. (English) Zbl 0944.00022 J. Symb. Comput. 28, No. 6, 737-845 (1999). MSC: 00B15 33-06 65-06 68-06 PDFBibTeX XMLCite \textit{R. A. Askey} (ed.) et al., J. Symb. Comput. 28, No. 6, 737--845 (1999; Zbl 0944.00022) Full Text: DOI
Ciccoli, Nicola; Koelink, Erik; Koornwinder, Tom H. \(q\)-Laguerre polynomials and big \(q\)-Bessel functions and their orthogonality relations. (English) Zbl 0964.33008 Methods Appl. Anal. 6, No. 1, 109-127 (1999). Reviewer: R.Koekoek (Delft) MSC: 33D45 33D80 17B37 PDFBibTeX XMLCite \textit{N. Ciccoli} et al., Methods Appl. Anal. 6, No. 1, 109--127 (1999; Zbl 0964.33008) Full Text: DOI arXiv
Koornwinder, Tom H. Special functions associated with root systems: a first introduction for non-specialists. (English) Zbl 0924.33008 Srinivasa Rao, K. (ed.) et al., Special functions and differential equations. Proceedings of a workshop, WSSF ’97, Madras, India, January 13–24, 1997. New Delhi: Allied Publishers Private Limited. 10-24 (1998). Reviewer: Som Prakash Goyal (Jaipur) MSC: 33C52 33D52 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, in: Special functions and differential equations. Proceedings of a workshop, WSSF '97, Madras, India, January 13--24, 1997. New Delhi: Allied Publishers Private Limited. 10--24 (1998; Zbl 0924.33008)
Stokman, J. V.; Koornwinder, T. H. On some limit cases of Askey-Wilson polynomials. (English) Zbl 0913.33008 J. Approximation Theory 95, No. 2, 310-330 (1998). Reviewer: D.Duverney (Lille) MSC: 33D45 PDFBibTeX XMLCite \textit{J. V. Stokman} and \textit{T. H. Koornwinder}, J. Approx. Theory 95, No. 2, 310--330 (1998; Zbl 0913.33008) Full Text: DOI
Koornwinder, T. H.; Schwartz, A. L. Product formulas and associated hypergroups for orthogonal polynomials on the simplex and on a parabolic biangle. (English) Zbl 0937.33009 Constructive Approximation 13, No. 4, 537-567 (1997). Reviewer: E.Stade (MR 99b:33024) MSC: 33C70 33C50 43A62 PDFBibTeX XMLCite \textit{T. H. Koornwinder} and \textit{A. L. Schwartz}, Constr. Approx. 13, No. 4, 537--567 (1997; Zbl 0937.33009) Full Text: DOI Link
Stokman, Jasper V.; Koornwinder, Tom H. Limit transitions for BC type multivariable orthogonal polynomials. (English) Zbl 0881.33026 Can. J. Math. 49, No. 2, 373-404 (1997). Reviewer: D.M.Bressoud (St.Paul) MSC: 33D80 33D45 33C50 PDFBibTeX XMLCite \textit{J. V. Stokman} and \textit{T. H. Koornwinder}, Can. J. Math. 49, No. 2, 373--404 (1997; Zbl 0881.33026) Full Text: DOI
Koornwinder, Tom H. Jacobi polynomials of type \(BC\), Jack polynomials, limit transitions and \(O(\infty)\). (English) Zbl 0968.33500 Ismail, Mourad E. H. (ed.) et al., Mathematical analysis, wavelets, and signal processing. An international conference on mathematical analysis and signal processing, Cairo University, Cairo, Egypt, January 3-9, 1994. Providence, RI: American Mathematical Society. Contemp. Math. 190, 283-286 (1995). MSC: 33C52 42C05 33C80 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Contemp. Math. 190, 283--286 (1995; Zbl 0968.33500) Full Text: arXiv
Koornwinder, Tom H. Compact quantum groups and \(q\)-special functions. (English) Zbl 0821.17015 Baldoni, Velleda (ed.) et al., Representations of Lie groups and quantum groups. Proceedings of the session of the European School of Group Theory, held in Trento, Italy, July 19-30, 1993. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 311, 46-128 (1994). Reviewer: A.Klimyk (Kiev) MSC: 17B37 16W30 33D15 33D45 46L89 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Pitman Res. Notes Math. Ser. 311, 46--128 (1994; Zbl 0821.17015)
Koornwinder, Tom H. q-Special functions, a tutorial. arXiv:math/9403216 Preprint, arXiv:math/9403216 [math.CA] (1994). MSC: 33-01 33-XX 40-XX 33D15 33D45 BibTeX Cite \textit{T. H. Koornwinder}, ``q-Special functions, a tutorial'', Preprint, arXiv:math/9403216 [math.CA] (1994) Full Text: arXiv OA License
Badertscher, Erich; Koornwinder, Tom H. Continuous Hahn polynomials of differential operator argument and analysis on Riemannian symmetric spaces of constant curvature. (English) Zbl 0759.33006 Can. J. Math. 44, No. 4, 750-773 (1992). Reviewer: R.Askey (Madison) MSC: 33C80 33C50 PDFBibTeX XMLCite \textit{E. Badertscher} and \textit{T. H. Koornwinder}, Can. J. Math. 44, No. 4, 750--773 (1992; Zbl 0759.33006) Full Text: DOI
Koornwinder, Tom H.; Swarttouw, René F. On \(q\)-analogues of the Fourier and Hankel transforms. (English) Zbl 0759.33007 Trans. Am. Math. Soc. 333, No. 1, 445-461 (1992). Reviewer: R.Askey (Madison) MSC: 33D15 42A38 42C05 PDFBibTeX XMLCite \textit{T. H. Koornwinder} and \textit{R. F. Swarttouw}, Trans. Am. Math. Soc. 333, No. 1, 445--461 (1992; Zbl 0759.33007) Full Text: DOI arXiv
Van Assche, Walter; Koornwinder, Tom H. Asymptotic behaviour for Wall polynomials and the addition formula for little \(q\)-Legendre polynomials. (English) Zbl 0738.33003 SIAM J. Math. Anal. 22, No. 1, 302-311 (1991). Reviewer: H.Exton (Dunrossness) MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{W. Van Assche} and \textit{T. H. Koornwinder}, SIAM J. Math. Anal. 22, No. 1, 302--311 (1991; Zbl 0738.33003) Full Text: DOI
Koornwinder, Tom H. The addition formula for little \(q\)-Legendre polynomials and the \(SU(2)\) quantum group. (English) Zbl 0738.33012 SIAM J. Math. Anal. 22, No. 1, 295-301 (1991). Reviewer: H.Exton (Dunrossness) MSC: 33D45 33D80 22E70 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, SIAM J. Math. Anal. 22, No. 1, 295--301 (1991; Zbl 0738.33012) Full Text: DOI
Koornwinder, Tom H. Jacobi functions as limit cases of q-ultraspherical polynomials. (English) Zbl 0713.33010 J. Math. Anal. Appl. 148, No. 1, 44-54 (1990). Reviewer: J.Faraut MSC: 33D45 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, J. Math. Anal. Appl. 148, No. 1, 44--54 (1990; Zbl 0713.33010) Full Text: DOI
Koornwinder, Tom H. Orthogonal polynomials in connection with quantum groups. (English) Zbl 0697.42019 Orthogonal polynomials: theory and practice, Proc. NATO ASI, Colombus/OH (USA) 1989, NATO ASI Ser., Ser. C 294, 257-292 (1990). MSC: 42C05 PDFBibTeX XML
Koelink, H. T.; Koornwinder, T. H. The Clebsch-Gordan coefficients for the quantum group \(S_{\mu}U(2)\) and q-Hahn polynomials. (English) Zbl 0708.22007 Indag. Math. 51, No. 4, 443-456 (1989). Reviewer: E.Kalnins MSC: 22E70 22E67 33C45 17B37 PDFBibTeX XMLCite \textit{H. T. Koelink} and \textit{T. H. Koornwinder}, Indag. Math. 51, No. 4, 443--456 (1989; Zbl 0708.22007)
Koornwinder, T. H. Representations of the twisted SU(2) quantum group and some q- hypergeometric orthogonal polynomials. (English) Zbl 0681.22020 Indag. Math. 51, No. 1, 97-117 (1989). Reviewer: A.Guts MSC: 22E70 22E65 33C80 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Indag. Math. 51, No. 1, 97--117 (1989; Zbl 0681.22020)
Koornwinder, Tom H. Research announcement. Continuous q-Legendre polynomials are spherical matrix elements of irreducible representations of the quantum SU(2) group. (English) Zbl 0677.33008 CWI Q. 2, No. 2, 171-173 (1989). Reviewer: R.Askey MSC: 33C45 33C80 20G05 22E45 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, CWI Q. 2, No. 2, 171--173 (1989; Zbl 0677.33008)
Koornwinder, Tom H. [Sharapudinov, I. I.] Meixner-Pollaczek polynomials and the Heisenberg algebra. (English) Zbl 0672.33011 J. Math. Phys. 30, No. 4, 767-769 (1989). Reviewer: R.Askey MSC: 33C45 33C80 81S05 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, J. Math. Phys. 30, No. 4, 767--769 (1989; Zbl 0672.33011) Full Text: DOI
Koornwinder, Tom H. Group theoretic interpretations of Askey’s scheme of hypergeometric orthogonal polynomials. (English) Zbl 0654.33006 Orthogonal polynomials and their applications, Proc. Int. Symp., Segovia/Spain 1986, Lect. Notes Math. 1329, 46-72 (1988). Reviewer: Charles F. Dunkl (Charlottesville) MSC: 33C45 43A80 44A20 PDFBibTeX XML
Koornwinder, T. H. A group theoretic interpretation of Wilson polynomials. (English) Zbl 0621.33018 Complex analysis and applications, Proc. Conf., Varna/Bulg. 1985, 335-355 (1986). Reviewer: Ch.F.Dunkel MSC: 33C45 43A85 PDFBibTeX XML
Askey, Richard; Koornwinder, Tom H.; Rahman, Mizan An intergral of products of ultraspherical functions and a q-extension. (English) Zbl 0564.33008 J. Lond. Math. Soc., II. Ser. 33, 133-148 (1986). MSC: 33C45 33C05 42C10 PDFBibTeX XMLCite \textit{R. Askey} et al., J. Lond. Math. Soc., II. Ser. 33, 133--148 (1986; Zbl 0564.33008) Full Text: DOI
Koornwinder, T. H. Special orthogonal polynomial systems mapped onto each other by the Fourier-Jacobi transform. (English) Zbl 0592.42005 Polynômes orthogonaux et applications, Proc. Laguerre Symp., Bar-le- Duc/France 1984, Lect. Notes Math. 1171, 174-183 (1985). Reviewer: A.N.Srivastava MSC: 42A20 42C05 33C10 33C80 33C45 PDFBibTeX XML
Koornwinder, Tom H. Matrix elements of irreducible representations of SU(2)\(\times SU(2)\) and vector-valued orthogonal polynomials. (English) Zbl 0581.22020 SIAM J. Math. Anal. 16, 602-613 (1985). Reviewer: W.Miller jun MSC: 22E70 81R10 33C45 33C80 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, SIAM J. Math. Anal. 16, 602--613 (1985; Zbl 0581.22020) Full Text: DOI
Koornwinder, Tom H. Jacobi functions and analysis on noncompact semisimple Lie groups. (English) Zbl 0584.43010 Special functions: Group theoretical aspects and applications, Math. Appl., D. Reidel Publ. Co. 18, 1-85 (1984). Reviewer: M.Flensted-Jensen MSC: 43A85 22E46 33C80 43-02 33C45 PDFBibTeX XML
Koornwinder, Tom H. Orthogonal polynomials with weight function \((1- x)^{\alpha}(1+x)^{\beta}+M\delta(x+1)+N\delta(x-1)\). (English) Zbl 0507.33005 Can. Math. Bull. 27, 205-214 (1984). MSC: 33C45 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Can. Math. Bull. 27, 205--214 (1984; Zbl 0507.33005) Full Text: DOI
Koornwinder, Tom H. Krawtchouk polynomials, a unification of two different group theoretic interpretations. (English) Zbl 0505.33015 SIAM J. Math. Anal. 13, 1011-1023 (1982). MSC: 33C80 33C45 33C55 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, SIAM J. Math. Anal. 13, 1011--1023 (1982; Zbl 0505.33015) Full Text: DOI
Koornwinder, T. H. Krawtchouk polynomials, a unification of two different group theoretic interpretations. (English) Zbl 0453.33009 Math. Cent., Amst., Afd. Zuivere Wiskd. ZW 156/81, 20 p. (1981). MSC: 33C80 33C45 33C55 PDFBibTeX XML
Flensted-Jensen, Mogens; Koornwinder, Tom H. Positive definite spherical functions on a non-compact, rank one symmetric space. (English) Zbl 0433.43014 Analyse harmonique sur les groupes de Lie II, Semin. Nancy-Strasbourg 1976-78, Lect. Notes Math. 739, 249-282 (1979). MSC: 43A90 33C45 22E46 PDFBibTeX XML
Flensted-Jensen, Mogens; Koornwinder, Tom H. Jacobi functions: the addition formula and the positivity of the dual convolution structure. (English) Zbl 0409.33009 Ark. Mat. 17, 139-151 (1979). MSC: 33C45 PDFBibTeX XMLCite \textit{M. Flensted-Jensen} and \textit{T. H. Koornwinder}, Ark. Mat. 17, 139--151 (1979; Zbl 0409.33009) Full Text: DOI
Koornwinder, Tom; Sprinkhuizen-Kuyper, Ida Generalized power series expansions for a class of orthogonal polynomials in two variables. (English) Zbl 0395.33008 SIAM J. Math. Anal. 9, 457-483 (1978). MSC: 33C45 33C05 PDFBibTeX XMLCite \textit{T. Koornwinder} and \textit{I. Sprinkhuizen-Kuyper}, SIAM J. Math. Anal. 9, 457--483 (1978; Zbl 0395.33008) Full Text: DOI
Koornwinder, Tom Positivity proofs for linearization and connection coefficients of orthogonal polynomials satisfying an addition formula. (English) Zbl 0386.33009 J. Lond. Math. Soc., II. Ser. 18, 101-114 (1978). MSC: 33C45 42C10 PDFBibTeX XMLCite \textit{T. Koornwinder}, J. Lond. Math. Soc., II. Ser. 18, 101--114 (1978; Zbl 0386.33009) Full Text: DOI
Koornwinder, Tom Yet another proof of the addition formula for Jacobi polynomials. (English) Zbl 0406.33006 J. Math. Anal. Appl. 61, 136-141 (1977). MSC: 33C45 33C80 PDFBibTeX XMLCite \textit{T. Koornwinder}, J. Math. Anal. Appl. 61, 136--141 (1977; Zbl 0406.33006) Full Text: DOI
Koornwinder, Tom The addition formula for Laguerre polynomials. (English) Zbl 0361.33002 SIAM J. Math. Anal. 8, 535-540 (1977). MSC: 33C45 PDFBibTeX XMLCite \textit{T. Koornwinder}, SIAM J. Math. Anal. 8, 535--540 (1977; Zbl 0361.33002) Full Text: DOI
Koornwinder, Tom Harmonics and spherical functions on Grassmann manifolds of rank two and two-variable analogues of Jacobi polynomials. (English) Zbl 0343.33009 Constr. Theory Funct. several Variables, Proc. Conf. Oberwolfach 1976, Lect. Notes Math. 571, 141-154 (1977). MSC: 33C45 33C80 43A90 43A85 PDFBibTeX XML
Koornwinder, Tom Jacobi polynomials. III: An analytic proof of the addition formula. (English) Zbl 0299.33012 SIAM J. Math. Anal. 6, 533-543 (1975). MSC: 33C45 33C10 33C55 33C05 PDFBibTeX XMLCite \textit{T. Koornwinder}, SIAM J. Math. Anal. 6, 533--543 (1975; Zbl 0299.33012) Full Text: DOI
Koornwinder, T. H. The addition formula for Jacobi polynomials and the theory of orthogonal polynomials in two variables, a survey. (English) Zbl 0297.33021 Math. Centrum, Amsterdam, Afd. toegepaste Wisk. TW 145/74, 17 p. (1974). MSC: 33C45 43A90 33C80 33C55 43A85 PDFBibTeX XML
Koornwinder, Tom H. Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators. III, IV. (English) Zbl 0291.33013 Nederl. Akad. Wet., Proc., Ser. A 77, 357-369 (1974); 77, 370-381 (1974). MSC: 33C47 42C05 33C80 43A90 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Nederl. Akad. Wet., Proc., Ser. A 77, 357--369, 370--381 (1974; Zbl 0291.33013)
Koornwinder, Tom H. Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators. I, II. (English) Zbl 0263.33011 Nederl. Akad. Wet., Proc., Ser. A 77, 48-58 (1974); 77, 59-66 (1974). MSC: 33C47 PDFBibTeX XML
Koornwinder, Tom Jacobi polynomials. II: An analytic proof of the product formula. (English) Zbl 0242.33020 SIAM J. Math. Anal. 5, 125-137 (1974). MSC: 33C45 33C10 PDFBibTeX XMLCite \textit{T. Koornwinder}, SIAM J. Math. Anal. 5, 125--137 (1974; Zbl 0242.33020) Full Text: DOI
Koornwinder, Tom Explicit formulas for special functions related to symmetric spaces. (English) Zbl 0288.33028 Harmonic Analysis homog. Spaces, Proc. Sympos. Pure Math. 26, Williamstown 1972, 351-354 (1973). MSC: 33C80 33C45 43A90 33C55 PDFBibTeX XML
Koornwinder, Tom The addition formula for Jacobi polynomials and spherical harmonics. (English) Zbl 0276.33023 SIAM J. appl. Math. 25, 236-246 (1973). MSC: 33C45 33C55 PDFBibTeX XMLCite \textit{T. Koornwinder}, SIAM J. Appl. Math. 25, 236--246 (1973; Zbl 0276.33023) Full Text: DOI
Flensted-Jensen, Mogens; Koornwinder, Tom The convolution structure for Jacobi function expansions. (English) Zbl 0267.42009 Ark. Mat. 11, 245-262 (1973). MSC: 42A38 44A15 44A35 33C45 43A90 PDFBibTeX XMLCite \textit{M. Flensted-Jensen} and \textit{T. Koornwinder}, Ark. Mat. 11, 245--262 (1973; Zbl 0267.42009) Full Text: DOI
Koornwinder, T. H. The addition formula for Jacobi polynomials. III: Completion of the proof. (English) Zbl 0247.33019 Math. Centrum, Amsterdam, Afd. toegepaste Wisk. TW 135/72, 11 p. (1972). MSC: 33C45 33C80 33C55 43A85 PDFBibTeX XML
Koornwinder, T. H. The addition formula for Jacobi polynomials. II: The Laplace type integral representation and the product formula. (English) Zbl 0247.33018 Math. Centrum, Amsterdam, Afd. toegepaste Wisk. TW 133/72, 29 p. (1972). MSC: 33C80 33C55 33C45 43A85 PDFBibTeX XML
Koornwinder, T. H. The addition formula for Jacobi polynomials. I: Summary of results. (English) Zbl 0247.33017 Nederl. Akad. Wet., Proc., Ser. A 75, 188-191 (1972). MSC: 33C45 33C55 33C80 43A85 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Nederl. Akad. Wet., Proc., Ser. A 75, 188--191 (1972; Zbl 0247.33017)
Koornwinder, T. H. The addition formula for Jacobi polynomials. I: Summary of results. (English) Zbl 0247.33016 Math. Centrum, Amsterdam, Afd. toegepaste Wisk. TW 131/71, 6 p. (1971). MSC: 33C45 33C55 43A85 33C80 PDFBibTeX XML
Dijksma, A.; Koornwinder, T. H. Spherical harmonics and the product of two Jacobi polynomials. (English) Zbl 0209.09302 Nederl. Akad. Wet., Proc., Ser. A 74, 191-196 (1971). MSC: 33C45 33C55 PDFBibTeX XMLCite \textit{A. Dijksma} and \textit{T. H. Koornwinder}, Nederl. Akad. Wet., Proc., Ser. A 74, 191--196 (1971; Zbl 0209.09302)