Kar, Pinaki Prasad; Gochhayat, Priyabrat Interlacing and bounds of zeros of quasi-orthogonal little \(q\)-Jacobi polynomials. (English) Zbl 07694963 Numer. Algorithms 93, No. 3, 1157-1170 (2023). MSC: 65-XX 33C45 33D15 33D45 PDFBibTeX XMLCite \textit{P. P. Kar} and \textit{P. Gochhayat}, Numer. Algorithms 93, No. 3, 1157--1170 (2023; Zbl 07694963) Full Text: DOI
Kar, Pinaki Prasad; Jordaan, Kerstin; Gochhayat, Priyabrat Stieltjes interlacing of zeros of little \(q\)-Jacobi and \(q\)-Laguerre polynomials from different sequences. (English) Zbl 07644408 Numer. Algorithms 92, No. 1, 723-746 (2023). MSC: 65-XX 33D15 33D45 PDFBibTeX XMLCite \textit{P. P. Kar} et al., Numer. Algorithms 92, No. 1, 723--746 (2023; Zbl 07644408) Full Text: DOI
Castillo, K.; Mbouna, D.; Petronilho, J. A characterization of continuous \(q\)-Jacobi, Chebyshev of the first kind and Al-Salam chihara polynomials. (English) Zbl 1493.33019 J. Math. Anal. Appl. 514, No. 2, Article ID 126358, 16 p. (2022). Reviewer: Roberto S. Costas-Santos (Alcalá) MSC: 33D45 42C05 PDFBibTeX XMLCite \textit{K. Castillo} et al., J. Math. Anal. Appl. 514, No. 2, Article ID 126358, 16 p. (2022; Zbl 1493.33019) Full Text: DOI arXiv
Forrester, Peter J. Global and local scaling limits for the \(\beta=2\) Stieltjes-Wigert random matrix ensemble. (English) Zbl 1501.15028 Random Matrices Theory Appl. 11, No. 2, Article ID 2250020, 26 p. (2022). Reviewer: Martín Argerami (Regina) MSC: 15B52 60B20 33D90 PDFBibTeX XMLCite \textit{P. J. Forrester}, Random Matrices Theory Appl. 11, No. 2, Article ID 2250020, 26 p. (2022; Zbl 1501.15028) Full Text: DOI arXiv
Masjed-Jamei, Mohammad; Soleyman, Fatemeh; Koepf, Wolfram Two finite sequences of symmetric \(q\)-orthogonal polynomials generated by two \(q\)-Sturm-Liouville problems. (English) Zbl 1527.39005 Rep. Math. Phys. 85, No. 1, 41-55 (2020). MSC: 39A13 39A27 05A30 33D05 33D45 PDFBibTeX XMLCite \textit{M. Masjed-Jamei} et al., Rep. Math. Phys. 85, No. 1, 41--55 (2020; Zbl 1527.39005) Full Text: DOI
Corteel, Sylvie; Kim, Jang Soo Lecture hall tableaux. (English) Zbl 1443.05182 Adv. Math. 371, Article ID 107266, 34 p. (2020). MSC: 05E10 05A15 33D45 33D50 05A30 PDFBibTeX XMLCite \textit{S. Corteel} and \textit{J. S. Kim}, Adv. Math. 371, Article ID 107266, 34 p. (2020; Zbl 1443.05182) Full Text: DOI arXiv
Kar, P. P.; Jordaan, K.; Gochhayat, P.; Kenfack Nangho, M. Quasi-orthogonality and zeros of some \({}_2 \phi_2\) and \({}_3 \phi_2\) polynomials. (English) Zbl 1443.33003 J. Comput. Appl. Math. 377, Article ID 112910, 12 p. (2020). Reviewer: István Mező (Debrecen) MSC: 33C05 33C45 33D15 33D45 PDFBibTeX XMLCite \textit{P. P. Kar} et al., J. Comput. Appl. Math. 377, Article ID 112910, 12 p. (2020; Zbl 1443.33003) Full Text: DOI arXiv
Raghavendar, K. Certain \(q\)-series identities and applications to lecture hall type partitions. (English) Zbl 1435.33019 J. Anal. 28, No. 1, 209-223 (2020). MSC: 33D15 33D45 05A30 PDFBibTeX XMLCite \textit{K. Raghavendar}, J. Anal. 28, No. 1, 209--223 (2020; Zbl 1435.33019) Full Text: DOI
Sun, Lisa Hui An extension of the Andrews-Warnaar partial theta function identity. (English) Zbl 1446.11071 Adv. Appl. Math. 115, Article ID 101985, 20 p. (2020). MSC: 11F27 33D15 PDFBibTeX XMLCite \textit{L. H. Sun}, Adv. Appl. Math. 115, Article ID 101985, 20 p. (2020; Zbl 1446.11071) Full Text: DOI arXiv
Groenevelt, Wolter A solution to the Al-Salam-Chihara moment problem. (English) Zbl 1501.47026 Buskes, Gerard (ed.) et al., Positivity and noncommutative analysis. Festschrift in honour of Ben de Pagter on the occasion of his 65th birthday. Based on the workshop “Positivity and Noncommutative Analysis”, Delft, The Netherlands, September 26–28, 2018. Cham: Birkhäuser. Trends Math., 223-248 (2019). Reviewer: Adhemar Bultheel (Leuven) MSC: 47A57 33C45 PDFBibTeX XMLCite \textit{W. Groenevelt}, in: Positivity and noncommutative analysis. Festschrift in honour of Ben de Pagter on the occasion of his 65th birthday. Based on the workshop ``Positivity and Noncommutative Analysis'', Delft, The Netherlands, September 26--28, 2018. Cham: Birkhäuser. 223--248 (2019; Zbl 1501.47026) Full Text: DOI arXiv
Dixit, Atul A simple proof of a congruence for a series involving the little \(q\)-Jacobi polynomials. (English) Zbl 1451.11108 Ann. Comb. 23, No. 3-4, 713-716 (2019). Reviewer: Mircea Merca (Cornu de Jos) MSC: 11P81 05A17 PDFBibTeX XMLCite \textit{A. Dixit}, Ann. Comb. 23, No. 3--4, 713--716 (2019; Zbl 1451.11108) Full Text: DOI arXiv
Olshanski, G. I. An analogue of the big \(q\)-Jacobi polynomials in the algebra of symmetric functions. (English. Russian original) Zbl 1381.33021 Funct. Anal. Appl. 51, No. 3, 204-220 (2017); translation from Funkts. Anal. Prilozh. 51, No. 3, 56-76 (2017). MSC: 33D45 05E05 PDFBibTeX XMLCite \textit{G. I. Olshanski}, Funct. Anal. Appl. 51, No. 3, 204--220 (2017; Zbl 1381.33021); translation from Funkts. Anal. Prilozh. 51, No. 3, 56--76 (2017) Full Text: DOI arXiv
Andrews, George E.; Dixit, Atul; Schultz, Daniel; Yee, Ae Ja Overpartitions related to the mock theta function \(\omega (q)\). (English) Zbl 1422.11210 Acta Arith. 181, No. 3, 253-286 (2017). MSC: 11P81 11P83 05A17 33D15 PDFBibTeX XMLCite \textit{G. E. Andrews} et al., Acta Arith. 181, No. 3, 253--286 (2017; Zbl 1422.11210) Full Text: DOI arXiv
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei Tridiagonal representations of the \(q\)-oscillator algebra and Askey-Wilson polynomials. (English) Zbl 1368.81074 J. Phys. A, Math. Theor. 50, No. 23, Article ID 235202, 15 p. (2017). MSC: 81Q10 17B81 33C45 33D45 47B36 PDFBibTeX XMLCite \textit{S. Tsujimoto} et al., J. Phys. A, Math. Theor. 50, No. 23, Article ID 235202, 15 p. (2017; Zbl 1368.81074) Full Text: DOI arXiv
Loureiro, Ana F.; Zeng, Jiang \(q\)-differential equations for \(q\)-classical polynomials and \(q\)-Jacobi-Stirling numbers. (English) Zbl 1336.33028 Math. Nachr. 289, No. 5-6, 693-717 (2016). MSC: 33C45 05A10 11B73 PDFBibTeX XMLCite \textit{A. F. Loureiro} and \textit{J. Zeng}, Math. Nachr. 289, No. 5--6, 693--717 (2016; Zbl 1336.33028) Full Text: DOI arXiv
Gochhayat, P.; Jordaan, K.; Raghavendar, K.; Swaminathan, A. Interlacing properties and bounds for zeros of \({}_2\phi_1\) hypergeometric and little \(q\)-Jacobi polynomials. (English) Zbl 1335.33002 Ramanujan J. 40, No. 1, 45-62 (2016). MSC: 33C05 33C45 33D15 PDFBibTeX XMLCite \textit{P. Gochhayat} et al., Ramanujan J. 40, No. 1, 45--62 (2016; Zbl 1335.33002) Full Text: DOI
Gorin, V. E.; Olshanski, G. I. Determinantal measures related to big \(q\)-Jacobi polynomials. (English. Russian original) Zbl 1376.60016 Funct. Anal. Appl. 49, No. 3, 214-217 (2015); translation from Funkts. Anal. Prilozh. 49, No. 3, 70-74 (2015). MSC: 60B99 60G55 33D45 PDFBibTeX XMLCite \textit{V. E. Gorin} and \textit{G. I. Olshanski}, Funct. Anal. Appl. 49, No. 3, 214--217 (2015; Zbl 1376.60016); translation from Funkts. Anal. Prilozh. 49, No. 3, 70--74 (2015) Full Text: DOI
Vinet, Luc; Yu, Guo-Fu; Zhedanov, Alexei \(-1\) Krall-Jacobi polynomials. (English) Zbl 1327.33003 Methods Appl. Anal. 22, No. 3, 249-258 (2015). MSC: 33C45 33C47 42C05 PDFBibTeX XMLCite \textit{L. Vinet} et al., Methods Appl. Anal. 22, No. 3, 249--258 (2015; Zbl 1327.33003) Full Text: DOI arXiv
Aldenhoven, Noud; Koelink, Erik; de los Ríos, Ana M. Matrix-valued little \(q\)-Jacobi polynomials. (English) Zbl 1318.33012 J. Approx. Theory 193, 164-183 (2015). Reviewer: Małgorzata Michalska (Lublin) MSC: 33C45 33C47 42C05 PDFBibTeX XMLCite \textit{N. Aldenhoven} et al., J. Approx. Theory 193, 164--183 (2015; Zbl 1318.33012) Full Text: DOI arXiv
Zhang, Ruiming; Chen, Li-Chen An operator approach to the inversion of certain Hankel matrices. (English) Zbl 1309.15011 Linear Algebra Appl. 470, 70-80 (2015). MSC: 15A09 15B05 33D45 15A15 PDFBibTeX XMLCite \textit{R. Zhang} and \textit{L.-C. Chen}, Linear Algebra Appl. 470, 70--80 (2015; Zbl 1309.15011) Full Text: DOI
Álvarez-Nodarse, R.; Adıgüzel, R. Sevinik On the limit of generalized non-standard \(q\)-Racah polynomials. (English) Zbl 1317.33014 J. Comput. Appl. Math. 259 B, 877-886 (2014). MSC: 33D45 PDFBibTeX XMLCite \textit{R. Álvarez-Nodarse} and \textit{R. S. Adıgüzel}, J. Comput. Appl. Math. 259, Part B, 877--886 (2014; Zbl 1317.33014) Full Text: DOI arXiv
Liu, Zhiguo A \(q\)-summation formula, the continuous \(q\)-Hahn polynomials and the big \(q\)-Jacobi polynomials. (English) Zbl 1329.33025 J. Math. Anal. Appl. 419, No. 2, 1045-1064 (2014). Reviewer: Kenier Castillo (Coimbra) MSC: 33D45 PDFBibTeX XMLCite \textit{Z. Liu}, J. Math. Anal. Appl. 419, No. 2, 1045--1064 (2014; Zbl 1329.33025) Full Text: DOI arXiv
Ismail, Mourad E. H.; Mansour, Zeinab S. I. Functions of the second kind for classical polynomials. (English) Zbl 1285.33013 Adv. Appl. Math. 54, 66-104 (2014). MSC: 33D45 33C45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{Z. S. I. Mansour}, Adv. Appl. Math. 54, 66--104 (2014; Zbl 1285.33013) Full Text: DOI
Area, I.; Atakishiyev, N.; Godoy, E.; Rodal, J. Linear partial \(q\)-difference equations on \(q\)-linear lattices and their bivariate \(q\)-orthogonal polynomial solutions. (English) Zbl 1329.39011 Appl. Math. Comput. 223, 520-536 (2013). MSC: 39A13 33D45 PDFBibTeX XMLCite \textit{I. Area} et al., Appl. Math. Comput. 223, 520--536 (2013; Zbl 1329.39011) Full Text: DOI arXiv
Lewanowicz, Stanisław; Woźny, Paweł; Nowak, Rafał Structure relations for the bivariate big \(q\)-Jacobi polynomials. (English) Zbl 1306.33022 Appl. Math. Comput. 219, No. 16, 8790-8802 (2013). Reviewer: Małgorzata Michalska (Lublin) MSC: 33C50 33C45 33D50 PDFBibTeX XMLCite \textit{S. Lewanowicz} et al., Appl. Math. Comput. 219, No. 16, 8790--8802 (2013; Zbl 1306.33022) Full Text: DOI
Guo, Victor J. W.; Ishikawa, Masao; Tagawa, Hiroyuki; Zeng, Jiang A generalization of Mehta-Wang determinant and Askey-Wilson polynomials. (English) Zbl 1294.05028 Proceedings of the 25th international conference on formal power series and algebraic combinatorics, FPSAC 2013, Paris, France, June 24–28, 2013. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). Discrete Mathematics and Theoretical Computer Science. Proceedings, 719-730, electronic only (2013). MSC: 05A30 05B45 15A15 PDFBibTeX XMLCite \textit{V. J. W. Guo} et al., in: Proceedings of the 25th international conference on formal power series and algebraic combinatorics, FPSAC 2013, Paris, France, June 24--28, 2013. Nancy: The Association. Discrete Mathematics \& Theoretical Computer Science (DMTCS). 719--730 (2013; Zbl 1294.05028) Full Text: arXiv Link
Atakishiyev, Natig; Atakishiyeva, Mesuma On discrete \(q\)-extensions of Chebyshev polynomials. (English) Zbl 1263.33009 Commun. Math. Anal. 14, No. 2, 1-12 (2013). MSC: 33D45 39A70 47B39 PDFBibTeX XMLCite \textit{N. Atakishiyev} and \textit{M. Atakishiyeva}, Commun. Math. Anal. 14, No. 2, 1--12 (2013; Zbl 1263.33009) Full Text: Euclid
Vinet, Luc; Zhedanov, Alexei A limit \(q=-1\) for the big \(q\)-Jacobi polynomials. (English) Zbl 1276.33019 Trans. Am. Math. Soc. 364, No. 10, 5491-5507 (2012). Reviewer: Alicia Cachafeiro López (Vigo) MSC: 33C45 33C47 42C05 33C05 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, Trans. Am. Math. Soc. 364, No. 10, 5491--5507 (2012; Zbl 1276.33019) Full Text: DOI arXiv
Ismail, Mourad E. H.; Koelink, Erik Spectral properties of operators using tridiagonalization. (English) Zbl 1248.33019 Anal. Appl., Singap. 10, No. 3, 327-343 (2012). MSC: 33C45 39A70 42C05 34L40 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{E. Koelink}, Anal. Appl., Singap. 10, No. 3, 327--343 (2012; Zbl 1248.33019) Full Text: DOI arXiv
Kyriakoussis, Andreas; Vamvakari, Malvina On terminating and non-terminating \(q\)-Gauss hypergeometric series distributions and the associated \(q\)-orthogonal polynomials. (English) Zbl 1246.60020 Fundam. Inform. 117, No. 1-4, 229-248 (2012). MSC: 60E05 60J10 33D45 PDFBibTeX XMLCite \textit{A. Kyriakoussis} and \textit{M. Vamvakari}, Fundam. Inform. 117, No. 1--4, 229--248 (2012; Zbl 1246.60020) Full Text: DOI
Moreno, Samuel G.; García-Caballero, Esther M. Non-classical orthogonality relations for continuous \(q\)-Jacobi polynomials. (English) Zbl 1237.33010 Taiwanese J. Math. 15, No. 4, 1677-1690 (2011). MSC: 33D45 42C05 PDFBibTeX XMLCite \textit{S. G. Moreno} and \textit{E. M. García-Caballero}, Taiwanese J. Math. 15, No. 4, 1677--1690 (2011; Zbl 1237.33010) Full Text: DOI
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
Vinet, Luc; Zhedanov, Alexei A Bochner theorem for Dunkl polynomials. (English) Zbl 1217.33022 SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 020, 9 p. (2011). MSC: 33C45 33C47 42C05 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 020, 9 p. (2011; Zbl 1217.33022) 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
Vinet, Luc; Zhedanov, Alexei A ’missing’ family of classical orthogonal polynomials. (English) Zbl 1222.33011 J. Phys. A, Math. Theor. 44, No. 8, Article ID 085201, 16 p. (2011). Reviewer: Sunil Dutt Purohit (Udaipur) MSC: 33C45 33C47 42C05 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, J. Phys. A, Math. Theor. 44, No. 8, Article ID 085201, 16 p. (2011; Zbl 1222.33011) Full Text: DOI arXiv
Ismail, Mourad E. H.; Obermaier, Josef Characterizations of continuous and discrete \(q\)-ultraspherical polynomials. (English) Zbl 1214.33010 Can. J. Math. 63, No. 1, 181-199 (2011). Reviewer: Nele De Schepper (Gent) MSC: 33D45 42C05 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{J. Obermaier}, Can. J. Math. 63, No. 1, 181--199 (2011; Zbl 1214.33010) Full Text: DOI
Andrews, George E. Parity in partition identities. (English) Zbl 1226.11107 Ramanujan J. 23, No. 1-3, 45-90 (2010). Reviewer: Jeremy Lovejoy (Paris) MSC: 11P81 05A17 05A19 11P83 11P84 PDFBibTeX XMLCite \textit{G. E. Andrews}, Ramanujan J. 23, No. 1--3, 45--90 (2010; Zbl 1226.11107) Full Text: DOI
Moreno, Samuel G.; García-Caballero, Esther M. Non-classical orthogonality relations for big and little \(q\)-Jacobi polynomials. (English) Zbl 1189.33031 J. Approx. Theory 162, No. 2, 303-322 (2010). Reviewer: Alicia Cachafeiro López (Vigo) MSC: 33D45 33D15 33C45 42C05 PDFBibTeX XMLCite \textit{S. G. Moreno} and \textit{E. M. García-Caballero}, J. Approx. Theory 162, No. 2, 303--322 (2010; Zbl 1189.33031) Full Text: DOI
Lewanowicz, Stanisław; Woźny, Paweł Two-variable orthogonal polynomials of big \(q\)-Jacobi type. (English) Zbl 1190.33018 J. Comput. Appl. Math. 233, No. 6, 1554-1561 (2010). Reviewer: Valery V. Karachik (Chelyabinsk) MSC: 33D50 33C50 PDFBibTeX XMLCite \textit{S. Lewanowicz} and \textit{P. Woźny}, J. Comput. Appl. Math. 233, No. 6, 1554--1561 (2010; Zbl 1190.33018) Full Text: DOI
Ernst, Thomas \(q\)-calculus as operational algebra. (English) Zbl 1209.33015 Proc. Est. Acad. Sci. 58, No. 2, 73-97 (2009). Reviewer: Osman Yürekli (Ithaca) MSC: 33D15 33C65 47E05 PDFBibTeX XMLCite \textit{T. Ernst}, Proc. Est. Acad. Sci. 58, No. 2, 73--97 (2009; Zbl 1209.33015) Full Text: DOI
Groenevelt, Wolter The vector-valued big \(q\)-Jacobi transform. (English) Zbl 1194.33019 Constr. Approx. 29, No. 1, 85-127 (2009). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33D45 47B25 44A15 47B39 PDFBibTeX XMLCite \textit{W. Groenevelt}, Constr. Approx. 29, No. 1, 85--127 (2009; Zbl 1194.33019) Full Text: DOI arXiv
Lewanowicz, Stanisław; Woźny, Paweł; Area, Iván; Godoy, Eduardo Multivariate generalized Bernstein polynomials: Identities for orthogonal polynomials of two variables. (English) Zbl 1183.33021 Numer. Algorithms 49, No. 1-4, 199-220 (2008). Reviewer: Thomas Stoll (Marseille) MSC: 33C50 33D50 65D17 PDFBibTeX XMLCite \textit{S. Lewanowicz} et al., Numer. Algorithms 49, No. 1--4, 199--220 (2008; Zbl 1183.33021) Full Text: DOI
Rosengren, Hjalmar Schur \(Q\)-polynomials, multiple hypergeometric series and enumeration of marked shifted tableaux. (English) Zbl 1202.33024 J. Comb. Theory, Ser. A 115, No. 3, 376-406 (2008). MSC: 33D45 05E10 PDFBibTeX XMLCite \textit{H. Rosengren}, J. Comb. Theory, Ser. A 115, No. 3, 376--406 (2008; Zbl 1202.33024) Full Text: DOI arXiv
Hounkonnou, M. N.; Nkouankam, E. B. Ngompe Factorization of the \(q\)-difference equation for continuous \(q\)-Jacobi polynomials. (English) Zbl 1134.39019 J. Phys. A, Math. Theor. 41, No. 4, Article ID 045202, 7 p. (2008). MSC: 39A13 33C45 PDFBibTeX XMLCite \textit{M. N. Hounkonnou} and \textit{E. B. N. Nkouankam}, J. Phys. A, Math. Theor. 41, No. 4, Article ID 045202, 7 p. (2008; Zbl 1134.39019) Full Text: DOI
Ernst, Thomas \(q\)-calculus as operational algebra. (English) Zbl 1148.33010 Ruffing, A. (ed.) et al., Communications of the Laufen colloquium on science, Laufen, Austria, April 1–5, 2007. Aachen: Shaker (ISBN 978-3-8322-6739-1/pbk). Berichte aus der Mathematik, 7.1-7.31 (2007). Reviewer: C. L. Parihar (Indore) MSC: 33D05 33D45 33D50 PDFBibTeX XMLCite \textit{T. Ernst}, in: Communications of the Laufen colloquium on science, Laufen, Austria, April 1--5, 2007. Aachen: Shaker. 7.1--7.31 (2007; Zbl 1148.33010)
Postelmans, Kelly; Van Assche, Walter Irrationality of \(\zeta _{q}(1)\) and \(\zeta _{q}(2)\). (English) Zbl 1138.11027 J. Number Theory 126, No. 1, 119-154 (2007). Reviewer: Wadim Zudilin (Moskva) MSC: 11J72 11M06 11M41 11J82 33D45 41A28 42C05 PDFBibTeX XMLCite \textit{K. Postelmans} and \textit{W. Van Assche}, J. Number Theory 126, No. 1, 119--154 (2007; Zbl 1138.11027) 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
Bouzeffour, Fethi A \(q\)-sampling theorem and product formula for continuous \(q\)-Jacobi functions. (English) Zbl 1122.33009 Proc. Am. Math. Soc. 135, No. 7, 2131-2139 (2007). Reviewer: Nicolae Cotfas (Bucureşti) MSC: 33D05 33D15 33D90 33C10 PDFBibTeX XMLCite \textit{F. Bouzeffour}, Proc. Am. Math. Soc. 135, No. 7, 2131--2139 (2007; Zbl 1122.33009) Full Text: DOI
Lewanowicz, Stanisław; Woźny, Paweł Dual generalized Bernstein basis. (English) Zbl 1087.41007 J. Approximation Theory 138, No. 2, 129-150 (2006). Reviewer: Jeremy Lovejoy (Paris) MSC: 41A10 33D45 PDFBibTeX XMLCite \textit{S. Lewanowicz} and \textit{P. Woźny}, J. Approx. Theory 138, No. 2, 129--150 (2006; Zbl 1087.41007) Full Text: DOI
Kadell, Kevin W. J. The little \(q\)-Jacobi functions of complex order. (English) Zbl 1219.33024 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, 301-338 (2005). MSC: 33D45 05A15 05A30 PDFBibTeX XMLCite \textit{K. W. J. Kadell}, Dev. Math. 13, 301--338 (2005; Zbl 1219.33024) Full Text: DOI
Obermaier, Josef; Szwarc, Ryszard Polynomial bases for continuous function spaces. (English) Zbl 1090.46505 Mache, Detlef H. (ed.) et al., Trends and applications in constructive approximation. Papers of the 4th IBoMAT meeting, Witten-Bommerholz, Germany, February 15–19, 2004. Basel: Birkhäuser (ISBN 3-7643-7124-2/hbk). ISNM. International Series of Numerical Mathematics 151, 195-205 (2005). Reviewer: Stamatis Koumandos (Nicosia) MSC: 46E15 46B15 33C45 33D45 PDFBibTeX XMLCite \textit{J. Obermaier} and \textit{R. Szwarc}, ISNM, Int. Ser. Numer. Math. 151, 195--205 (2005; Zbl 1090.46505)
Kyriakoussis, A.; Vamvakari, M. G. Generalization of matching extensions in graphs – combinatorial interpretation of orthogonal and \(q\)-orthogonal polynomials. (English) Zbl 1066.05112 Discrete Math. 296, No. 2-3, 199-209 (2005). MSC: 05C70 05C38 05E35 33C45 PDFBibTeX XMLCite \textit{A. Kyriakoussis} and \textit{M. G. Vamvakari}, Discrete Math. 296, No. 2--3, 199--209 (2005; Zbl 1066.05112) Full Text: DOI
Atakishiyev, N. M.; Klimyk, A. U. On discrete \(q\)-ultraspherical polynomials and their duals. (English) Zbl 1076.33013 J. Math. Anal. Appl. 306, No. 2, 637-645 (2005). Reviewer: Angela Pasquale (Metz) MSC: 33D45 PDFBibTeX XMLCite \textit{N. M. Atakishiyev} and \textit{A. U. Klimyk}, J. Math. Anal. Appl. 306, No. 2, 637--645 (2005; Zbl 1076.33013) Full Text: DOI arXiv
Postelmans, Kelly; Van Assche, Walter Multiple little \(q\)-Jacobi polynomials. (English) Zbl 1068.33031 J. Comput. Appl. Math. 178, No. 1-2, 361-375 (2005). Reviewer: Youssef Ben Cheikh (Monastir) MSC: 33D45 42C05 PDFBibTeX XMLCite \textit{K. Postelmans} and \textit{W. Van Assche}, J. Comput. Appl. Math. 178, No. 1--2, 361--375 (2005; Zbl 1068.33031) Full Text: DOI arXiv
Groenevelt, Wolter Bilinear summation formulas from quantum algebra representations. (English) Zbl 1068.33029 Ramanujan J. 8, No. 3, 383-416 (2004). Reviewer: J. Saurer (Regensburg) MSC: 33D45 PDFBibTeX XMLCite \textit{W. Groenevelt}, Ramanujan J. 8, No. 3, 383--416 (2004; Zbl 1068.33029) Full Text: DOI arXiv
Area, I.; Godoy, E.; Woźny, P.; Lewanowicz, S.; Ronveaux, A. Formulae relating little \(q\)-Jacobi, \(q\)-Hahn and \(q\)-Bernstein polynomials: Application to \(q\)-Bézier curve evaluation. (English) Zbl 1065.33010 Integral Transforms Spec. Funct. 15, No. 5, 375-385 (2004). Reviewer: Stamatis Koumandos (Nicosia) MSC: 33D45 65D17 PDFBibTeX XMLCite \textit{I. Area} et al., Integral Transforms Spec. Funct. 15, No. 5, 375--385 (2004; Zbl 1065.33010) Full Text: DOI
Atakishiyev, N. M.; Klimyk, A. U. On \(q\)-orthogonal polynomials, dual to little and big \(q\)-Jacobi polynomials. (English) Zbl 1049.33013 J. Math. Anal. Appl. 294, No. 1, 246-257 (2004). Reviewer: Stamatis Koumandos (Nicosia) MSC: 33D45 33D90 PDFBibTeX XMLCite \textit{N. M. Atakishiyev} and \textit{A. U. Klimyk}, J. Math. Anal. Appl. 294, No. 1, 246--257 (2004; Zbl 1049.33013) Full Text: DOI arXiv
Lewanowicz, Stanisław; Woźny, Paweł Generalized Bernstein polynomials. (English) Zbl 1045.41003 BIT 44, No. 1, 63-78 (2004). Reviewer: Jeremy Lovejoy (Talence) MSC: 41A10 33D45 PDFBibTeX XMLCite \textit{S. Lewanowicz} and \textit{P. Woźny}, BIT 44, No. 1, 63--78 (2004; Zbl 1045.41003) Full Text: DOI
Ismail, Mourad E. H. Difference equations and quantized discriminants for \(q\)-orthogonal polynomials. (English) Zbl 1032.33012 Adv. Appl. Math. 30, No. 3, 562-589 (2003). Reviewer: Youssef Ben Cheikh (Monastir) MSC: 33D45 PDFBibTeX XMLCite \textit{M. E. H. Ismail}, Adv. Appl. Math. 30, No. 3, 562--589 (2003; Zbl 1032.33012) Full Text: DOI
Koelink, Erik; Stokman, Jasper V. The big \(q\)-Jacobi function transform. (English) Zbl 1048.33014 Constructive Approximation 19, No. 2, 191-235 (2003). Reviewer: Angela Pasquale (Metz) MSC: 33D45 47B25 47B39 33D80 PDFBibTeX XMLCite \textit{E. Koelink} and \textit{J. V. Stokman}, Constr. Approx. 19, No. 2, 191--235 (2003; Zbl 1048.33014) Full Text: DOI arXiv
Area, I.; Godoy, E.; Marcellán, F. \(q\)-coherent pairs and \(q\)-orthogonal polynomials. (English) Zbl 1020.33005 Appl. Math. Comput. 128, No. 2-3, 191-216 (2002). Reviewer: Som Prakash Goyal (Jaipur) MSC: 33D45 33D15 PDFBibTeX XMLCite \textit{I. Area} et al., Appl. Math. Comput. 128, No. 2--3, 191--216 (2002; Zbl 1020.33005) Full Text: DOI
Koepf, Wolfram; Schmersau, Dieter On a structure formula for classical \(q\)-orthogonal polynomials. (English) Zbl 1004.33008 J. Comput. Appl. Math. 136, No. 1-2, 99-107 (2001). Reviewer: Christian Krattenthaler (Wien) MSC: 33D45 33C45 PDFBibTeX XMLCite \textit{W. Koepf} and \textit{D. Schmersau}, J. Comput. Appl. Math. 136, No. 1--2, 99--107 (2001; Zbl 1004.33008) Full Text: DOI arXiv
Vinet, Luc; Yermolayeva, Oksana; Zhedanov, Alexei A method to study the Krall and \(q\)-Krall polynomials. (English) Zbl 0990.33011 J. Comput. Appl. Math. 133, No. 1-2, 647-656 (2001). Reviewer: Roelof Koekoek (Delft) MSC: 33C45 33D45 PDFBibTeX XMLCite \textit{L. Vinet} et al., J. Comput. Appl. Math. 133, No. 1--2, 647--656 (2001; Zbl 0990.33011) Full Text: DOI
Ismail, Mourad E. H.; Simeonov, Plamen C. The spectrum of an integral operator in weighted \(L_ 2\) spaces. (English) Zbl 1059.47505 Pac. J. Math. 198, No. 2, 443-476 (2001). MSC: 47B39 47A70 47G10 33D45 33D90 39A13 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{P. C. Simeonov}, Pac. J. Math. 198, No. 2, 443--476 (2001; Zbl 1059.47505) Full Text: DOI
Takeyama, Yoshihiro The \(q\)-twisted cohomology and the \(q\)-hypergeometric function at \(|q|=1\). (English) Zbl 0980.33014 Publ. Res. Inst. Math. Sci. 37, No. 1, 71-89 (2001). Reviewer: David M. Bressoud (Saint Paul) MSC: 33D60 33D05 33D45 PDFBibTeX XMLCite \textit{Y. Takeyama}, Publ. Res. Inst. Math. Sci. 37, No. 1, 71--89 (2001; Zbl 0980.33014) Full Text: DOI arXiv Euclid
Vinet, Luc; Zhedanov, Alexei Generalized little \(q\)-Jacobi polynomials as eigensolutions of higher-order \(q\)-difference operators. (English) Zbl 0973.33009 Proc. Am. Math. Soc. 129, No. 5, 1317-1327 (2001). Reviewer: Roelof Koekoek (Delft) MSC: 33D45 39A13 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, Proc. Am. Math. Soc. 129, No. 5, 1317--1327 (2001; Zbl 0973.33009) Full Text: DOI
Kim, Dongsu; Zeng, Jiang On a continued fraction formula of Wall. (English) Zbl 0971.05006 Ramanujan J. 4, No. 4, 421-427 (2000). MSC: 05A15 05A30 33D45 PDFBibTeX XMLCite \textit{D. Kim} and \textit{J. Zeng}, Ramanujan J. 4, No. 4, 421--427 (2000; Zbl 0971.05006) Full Text: DOI
Lewanowicz, Stanislaw Recursion formulae for basic hypergeometric functions. (English) Zbl 0960.33008 J. Comput. Appl. Math. 121, No. 1-2, 297-312 (2000). Reviewer: Roelof Koekoek (Delft) MSC: 33D15 PDFBibTeX XMLCite \textit{S. Lewanowicz}, J. Comput. Appl. Math. 121, No. 1--2, 297--312 (2000; Zbl 0960.33008) Full Text: DOI
Baker, T. H.; Forrester, P. J. Multivariable Al-Salam & Carlitz polynomials associated with the type \(A\;q\)-Dunkl kernel. (English) Zbl 0970.33012 Math. Nachr. 212, 5-35 (2000). Reviewer: Hjalmar Rosengren (Göteborg) MSC: 33D45 PDFBibTeX XMLCite \textit{T. H. Baker} and \textit{P. J. Forrester}, Math. Nachr. 212, 5--35 (2000; Zbl 0970.33012) Full Text: DOI arXiv
Stokman, Jasper V. On \(BC\) type basic hypergeometric orthogonal polynomials. (English) Zbl 0936.33008 Trans. Am. Math. Soc. 352, No. 4, 1527-1579 (2000). Reviewer: Wolfram Koepf (Leipzig) MSC: 33D52 33D45 33D80 PDFBibTeX XMLCite \textit{J. V. Stokman}, Trans. Am. Math. Soc. 352, No. 4, 1527--1579 (2000; Zbl 0936.33008) Full Text: DOI arXiv
Dijkhuizen, Mathijs S.; Stokman, Jasper V. Some limit transitions between BC type orthogonal polynomials interpreted on quantum complex Grassmannians. (English) Zbl 0960.33010 Publ. Res. Inst. Math. Sci. 35, No. 3, 451-500 (1999). Reviewer: A.Klimyk (Kyïv) MSC: 33D80 33D45 17B37 81R50 PDFBibTeX XMLCite \textit{M. S. Dijkhuizen} and \textit{J. V. Stokman}, Publ. Res. Inst. Math. Sci. 35, No. 3, 451--500 (1999; Zbl 0960.33010) Full Text: DOI arXiv
Floris, Paul G. A. Addition theorems for spherical polynomials on a family of quantum spheres. (English) Zbl 0938.33009 van Diejen, Jan Felipe (ed.) et al., Algebraic methods and \(q\)-special functions. Providence, RI: American Mathematical Society. CRM Proc. Lect. Notes. 22, 145-170 (1999). Reviewer: J.Saurer (Regensburg) MSC: 33D45 33D80 16W30 17B37 81R50 PDFBibTeX XMLCite \textit{P. G. A. Floris}, in: Algebraic methods and \(q\)-special functions. Providence,~RI: American Mathematical Society. 145--170 (1999; Zbl 0938.33009)
Rahman, Mizan; Tariq, Qazi M. Addition formulas for \(q\)-Legendre-type functions. (English) Zbl 0949.33014 Methods Appl. Anal. 6, No. 1, 3-20 (1999). Reviewer: R.P.Agarwal (Lucknow) MSC: 33D80 33D45 33D15 PDFBibTeX XMLCite \textit{M. Rahman} and \textit{Q. M. Tariq}, Methods Appl. Anal. 6, No. 1, 3--20 (1999; Zbl 0949.33014) Full Text: DOI
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
Dijkhuizen, Mathijs S.; Noumi, Masatoshi A family of quantum projective spaces and related \(q\)-hypergeometric orthogonal polynomials. (English) Zbl 0906.33011 Trans. Am. Math. Soc. 350, No. 8, 3269-3296 (1998). MSC: 33D80 33D45 17B37 81R50 PDFBibTeX XMLCite \textit{M. S. Dijkhuizen} and \textit{M. Noumi}, Trans. Am. Math. Soc. 350, No. 8, 3269--3296 (1998; Zbl 0906.33011) Full Text: DOI arXiv
Floris, P. G. A.; Koelink, H. T. A commuting \(q\)-analogue of the addition formula for disk polynomials. (English) Zbl 0905.33012 Constructive Approximation 13, No. 4, 511-535 (1997). Reviewer: N.M.Temme (Amsterdam) MSC: 33D80 33D20 PDFBibTeX XMLCite \textit{P. G. A. Floris} and \textit{H. T. Koelink}, Constr. Approx. 13, No. 4, 511--535 (1997; Zbl 0905.33012) Full Text: DOI arXiv
Kirillov, Alexander A. jun. Lectures on affine Hecke algebras and Macdonald’s conjectures. (English) Zbl 0884.05100 Bull. Am. Math. Soc., New Ser. 34, No. 3, 251-292 (1997). MSC: 05E35 33D80 05A19 PDFBibTeX XMLCite \textit{A. A. Kirillov jun.}, Bull. Am. Math. Soc., New Ser. 34, No. 3, 251--292 (1997; Zbl 0884.05100) Full Text: DOI arXiv
Floris, Paul G. A. Addition formula for \(q\)-disk polynomials. (English) Zbl 0891.33009 Compos. Math. 108, No. 2, 123-149 (1997). MSC: 33D45 33D80 81R50 17B37 16W30 PDFBibTeX XMLCite \textit{P. G. A. Floris}, Compos. Math. 108, No. 2, 123--149 (1997; Zbl 0891.33009) Full Text: DOI arXiv
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
Ismail, Mourad E. H.; Masson, David R.; Suslov, Sergei K. Some generating functions for \(q\)-polynomials. (English) Zbl 0873.33014 Ismail, Mourad E. H. (ed.) et al., Special functions, \(q\)-series and related topics. Providence, RI: American Mathematical Society. Fields Inst. Commun. 14, 91-108 (1997). Reviewer: A.N.Srivastava (Puna) MSC: 33D45 33D15 33C45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} et al., Fields Inst. Commun. 14, 91--108 (1997; Zbl 0873.33014)
Stokman, Jasper V. Multivariable big and little \(q\)-Jacobi polynomials. (English) Zbl 0892.33010 SIAM J. Math. Anal. 28, No. 2, 453-480 (1997). Reviewer: P.K.Banerji (Jodhpur) MSC: 33D45 33D80 PDFBibTeX XMLCite \textit{J. V. Stokman}, SIAM J. Math. Anal. 28, No. 2, 453--480 (1997; Zbl 0892.33010) Full Text: DOI
Floreanini, Roberto; LeTourneux, Jean; Vinet, Luc A \(q\)-deformed \(e(4)\) and continuous \(q\)-Jacobi polynomials. (English) Zbl 0870.17009 J. Math. Phys. 37, No. 8, 4135-4149 (1996). MSC: 17B37 33D80 PDFBibTeX XMLCite \textit{R. Floreanini} et al., J. Math. Phys. 37, No. 8, 4135--4149 (1996; Zbl 0870.17009) Full Text: DOI
Berg, Christian; Ismail, Mourad E. H. \(q\)-Hermite polynomials and classical orthogonal polynomials. (English) Zbl 0858.33015 Can. J. Math. 48, No. 1, 43-63 (1996). Reviewer: A.K.Agarwal (Grambling) MSC: 33D45 33C45 44A60 PDFBibTeX XMLCite \textit{C. Berg} and \textit{M. E. H. Ismail}, Can. J. Math. 48, No. 1, 43--63 (1996; Zbl 0858.33015) Full Text: DOI arXiv
Khan, Mumtaz Ahmad On some operational representations of \(q\)-polynomials. (English) Zbl 0836.33009 Czech. Math. J. 45, No. 3, 457-464 (1995). Reviewer: H.Exton (Dunrossness) MSC: 33D45 33D60 PDFBibTeX XMLCite \textit{M. A. Khan}, Czech. Math. J. 45, No. 3, 457--464 (1995; Zbl 0836.33009) Full Text: EuDML
Freund, Peter G. O.; Zabrodin, Anton V. The spectral problem for the \(q\)-Knizhnik-Zamolodchikov equation and continuous \(q\)-Jacobi polynomials. (English) Zbl 0832.35106 Commun. Math. Phys. 173, No. 1, 17-42 (1995). MSC: 35P25 82B23 35Q58 81U20 81T30 33D45 PDFBibTeX XMLCite \textit{P. G. O. Freund} and \textit{A. V. Zabrodin}, Commun. Math. Phys. 173, No. 1, 17--42 (1995; Zbl 0832.35106) Full Text: DOI arXiv
Lance, E. Christopher An explicit description of the fundamental unitary for \(SU(2)_ q\). (English) Zbl 0818.17014 Commun. Math. Phys. 164, No. 1, 1-15 (1994). MSC: 17B37 33D45 46L89 PDFBibTeX XMLCite \textit{E. C. Lance}, Commun. Math. Phys. 164, No. 1, 1--15 (1994; Zbl 0818.17014) Full Text: DOI
Simion, R.; Stanton, D. Specializations of generalized Laguerre polynomials. (English) Zbl 0813.05074 SIAM J. Math. Anal. 25, No. 2, 712-719 (1994). Reviewer: C.Malvenuto (Roma) MSC: 05E35 33C65 PDFBibTeX XMLCite \textit{R. Simion} and \textit{D. Stanton}, SIAM J. Math. Anal. 25, No. 2, 712--719 (1994; Zbl 0813.05074) Full Text: DOI arXiv
Khan, Mumtaz Ahmad On some operational generating formulae. (English) Zbl 0831.33011 Acta Cienc. Indica, Math. 19, No. 1, 35-38 (1993). Reviewer: A.K.Agarwal (Grambling) MSC: 33D45 33D65 PDFBibTeX XMLCite \textit{M. A. Khan}, Acta Cienc. Indica, Math. 19, No. 1, 35--38 (1993; Zbl 0831.33011)
Noumi, Masatoshi; Yamada, Hirofumi; Mimachi, Katsuhisa Finite dimensional representations of the quantum group \(GL_ q(n;\mathbb{C})\) and the zonal spherical functions on \(U_ q(n-1)\setminus U_ q(n)\). (English) Zbl 0806.17016 Jap. J. Math., New Ser. 19, No. 1, 31-80 (1993). Reviewer: A.Klimyk (Kiev) MSC: 17B37 33D55 PDFBibTeX XMLCite \textit{M. Noumi} et al., Jpn. J. Math., New Ser. 19, No. 1, 31--80 (1993; Zbl 0806.17016)
Koornwinder, Tom H. Askey-Wilson polynomials as zonal spherical functions on the \(SU(2)\) quantum group. (English) Zbl 0799.33015 SIAM J. Math. Anal. 24, No. 3, 795-813 (1993). MSC: 33D70 33D80 17B37 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, SIAM J. Math. Anal. 24, No. 3, 795--813 (1993; Zbl 0799.33015) Full Text: DOI
Kumar, Rajendra; Saxena, R. K.; Srivastava, H. M. Fractional \(q\)-derivatives and a class of expansions of basic hypergeometric functions. (English) Zbl 0779.33010 Simon Stevin 66, No. 3-4, 295-311 (1992). Reviewer: R.Kumar (Victoria) MSC: 33D20 33D45 26A33 PDFBibTeX XMLCite \textit{R. Kumar} et al., Simon Stevin 66, No. 3--4, 295--311 (1992; Zbl 0779.33010)
Noumi, Masatoshi; Mimachi, Katsuhisa Spherical functions on a family of quantum 3-spheres. (English) Zbl 0760.33009 Compos. Math. 83, No. 1, 19-42 (1992). Reviewer: A.Klimyk (Kiev) MSC: 33D80 33D45 17B37 43A90 PDFBibTeX XMLCite \textit{M. Noumi} and \textit{K. Mimachi}, Compos. Math. 83, No. 1, 19--42 (1992; Zbl 0760.33009) Full Text: Numdam EuDML
de Médicis, Anne; Viennot, Xavier G. Moments of \(q\)-Laguerre polynomials and the Foata-Zeilberger bijection. (Moments des \(q\)-polynômes de Laguerre et la bijection de Foata-Zeilberger.) (French. English summary) Zbl 0978.05544 Sémin. Lothar. Comb. 28, B28g, no pag. (1992). MSC: 05E35 33C45 11B65 PDFBibTeX XMLCite \textit{A. de Médicis} and \textit{X. G. Viennot}, Sémin. Lothar. Comb. 28, B28g, no pag. (1992; Zbl 0978.05544) Full Text: EMIS
Gupta, D. P.; Ismail, M. E. H.; Masson, D. R. Contiguous relations, basic hypergeometric functions, and orthogonal polynomials. II: Associated big \(q\)-Jacobi polynomials. (English) Zbl 0766.33016 J. Math. Anal. Appl. 171, No. 2, 477-497 (1992). Reviewer: M.G.de Bruin (Haarlem) MSC: 33D45 PDFBibTeX XMLCite \textit{D. P. Gupta} et al., J. Math. Anal. Appl. 171, No. 2, 477--497 (1992; Zbl 0766.33016) Full Text: DOI
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
Ismail, Mourad E. H.; Masson, David R.; Rahman, Mizan Complex weight functions for classical orthogonal polynomials. (English) Zbl 0752.33003 Can. J. Math. 43, No. 6, 1294-1308 (1991). Reviewer: R.P.Agarwal (Lucknow) MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{M. E. H. Ismail} et al., Can. J. Math. 43, No. 6, 1294--1308 (1991; Zbl 0752.33003) Full Text: DOI
Masuda, Tetsuya; Mimachi, Katsuhisa; Nakagami, Yoshiomi; Noumi, Masatoshi; Ueno, Kimio Representations of the quantum group \(SU_ q(2)\) and the little q-Jacobi polynomials. (English) Zbl 0737.33012 J. Funct. Anal. 99, No. 2, 357-386 (1991). Reviewer: A.Kaneko (Komaba) MSC: 33D80 33C45 22E45 17B37 PDFBibTeX XMLCite \textit{T. Masuda} et al., J. Funct. Anal. 99, No. 2, 357--386 (1991; Zbl 0737.33012) Full Text: DOI
Noumi, Masatoshi; Mimachi, Katsuhisa Big \(q\)-Jacobi polynomials, \(q\)-Hahn polynomials, and a family of quantum 3-spheres. (English) Zbl 0749.33010 Lett. Math. Phys. 19, No. 4, 299-305 (1990). Reviewer: R.A.Gustafson (College Station) MSC: 33D80 33D55 33D45 17B37 33C45 PDFBibTeX XMLCite \textit{M. Noumi} and \textit{K. Mimachi}, Lett. Math. Phys. 19, No. 4, 299--305 (1990; Zbl 0749.33010) Full Text: DOI
Ueno, Kimio Representation theory of quantum groups. (Japanese) Zbl 0718.17012 Sûgaku 42, No. 1, 68-73 (1990). Reviewer: H.Yamada (Tokyo) MSC: 17B37 17-02 81R50 33D80 PDFBibTeX XMLCite \textit{K. Ueno}, Sūgaku 42, No. 1, 68--73 (1990; Zbl 0718.17012)
Noumi, Masatoshi; Mimachi, Katsuhisa Quantum 2-spheres and big q-Jacobi polynomials. (English) Zbl 0699.33005 Commun. Math. Phys. 128, No. 3, 521-531 (1990). Reviewer: A.Kaneko MSC: 33C55 81R10 PDFBibTeX XMLCite \textit{M. Noumi} and \textit{K. Mimachi}, Commun. Math. Phys. 128, No. 3, 521--531 (1990; Zbl 0699.33005) Full Text: DOI