Jiménez-Pastor, Antonio; Petkovšek, Marko The factorial-basis method for finding definite-sum solutions of linear recurrences with polynomial coefficients. (English) Zbl 1539.33019 J. Symb. Comput. 117, 15-50 (2023). Reviewer: Christoph Koutschan (Linz) MSC: 33F10 39A06 68W30 11B83 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Marcellán, Francisco; Khalfallah, Mohamed On the characterizations of third-degree semiclassical forms via polynomial mappings. (English) Zbl 1527.33005 Integral Transforms Spec. Funct. 34, No. 1, 65-87 (2023). MSC: 33C45 42C05 × Cite Format Result Cite Review PDF Full Text: DOI
Castillo, K.; de Jesus, M. N.; Marcellán, F.; Petronilho, J. \(H_q\)-semiclassical orthogonal polynomials via polynomial mappings. (English) Zbl 1462.42043 Ramanujan J. 54, No. 1, 113-136 (2021). MSC: 42C05 33C45 05A30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Castillo, K.; de Jesus, M. N.; Petronilho, J. A note on orthogonal polynomials described by Chebyshev polynomials. (English) Zbl 1460.33007 J. Math. Anal. Appl. 497, No. 2, Article ID 124906, 7 p. (2021). Reviewer: Bujar Fejzullahu (Presevo) MSC: 33C45 42C05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Castillo, K.; de Jesus, M. N.; Petronilho, J. An electrostatic interpretation of the zeros of sieved ultraspherical polynomials. (English) Zbl 1443.33030 J. Math. Phys. 61, No. 5, 053501, 19 p. (2020). MSC: 33C47 42C05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Luo, Min-Jie; Wong, R. Asymptotics of the associated Pollaczek polynomials. (English) Zbl 1416.33018 Proc. Am. Math. Soc. 147, No. 6, 2583-2597 (2019). Reviewer: Francisco Pérez Acosta (La Laguna) MSC: 33C45 41A60 33C05 × Cite Format Result Cite Review PDF Full Text: DOI
Simanek, Brian Applications of a new formula for OPUC with periodic Verblunsky coefficients. (English) Zbl 1422.42040 Res. Math. Sci. 5, No. 4, Paper No. 42, 23 p. (2018). Reviewer: Pierluigi Vellucci (Roma) MSC: 42C05 33C45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Castillo, K.; de Jesus, M. N.; Petronilho, J. On semiclassical orthogonal polynomials via polynomial mappings. (English) Zbl 1370.33014 J. Math. Anal. Appl. 455, No. 2, 1801-1821 (2017). MSC: 33C47 42C05 × Cite Format Result Cite Review PDF Full Text: DOI
Baseilhac, P.; Gainutdinov, A. M.; Vu, T. T. Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials. (English) Zbl 1406.17022 Linear Algebra Appl. 522, 71-110 (2017). MSC: 17B37 17B81 33D80 42C05 81R10 81R12 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Tounsi, M. Ihsen; Raddaoui, Zouhaier On the cubic decomposition of a family of \(G_q\)-semiclassical polynomial sequences of class one. (English) Zbl 1342.33028 J. Difference Equ. Appl. 22, No. 3, 391-410 (2016). MSC: 33C45 42C05 × Cite Format Result Cite Review PDF Full Text: DOI
Maroni, Pascal; Mesquita, Teresa A. Cubic decomposition of 2-orthogonal polynomial sequences. (English) Zbl 1266.42069 Mediterr. J. Math. 10, No. 2, 843-863 (2013). MSC: 42C05 33C45 × Cite Format Result Cite Review PDF Full Text: DOI
Maroni, P.; Mesquita, T. A.; da Rocha, Z. On the general cubic decomposition of polynomial sequences. (English) Zbl 1232.33017 J. Difference Equ. Appl. 17, No. 9, 1303-1332 (2011). Reviewer: Roelof Koekoek (Delft) MSC: 33C45 42C05 × Cite Format Result Cite Review PDF Full Text: DOI
de Jesus, M. N.; Petronilho, J. On orthogonal polynomials obtained via polynomial mappings. (English) Zbl 1209.42018 J. Approx. Theory 162, No. 12, 2243-2277 (2010). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 42C05 33C45 × Cite Format Result Cite Review PDF Full Text: DOI
Petronilho, J. Orthogonal polynomials on the unit circle via a polynomial mapping on the real line. (English) Zbl 1225.42019 J. Comput. Appl. Math. 216, No. 1, 98-127 (2008). MSC: 42C05 33C45 × Cite Format Result Cite Review PDF Full Text: DOI
Chen, Yang; Griffin, James; Ismail, Mourad E. H. Generalizations of Chebyshev polynomials and polynomial mappings. (English) Zbl 1176.33011 Trans. Am. Math. Soc. 359, No. 10, 4787-4828 (2007). MSC: 33C45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
da Fonseca, C. M. On the location of the eigenvalues of Jacobi matrices. (English) Zbl 1176.15027 Appl. Math. Lett. 19, No. 11, 1168-1174 (2006). MSC: 15A42 15B05 42C05 26C10 × Cite Format Result Cite Review PDF Full Text: DOI
Rajković, Predrag M.; Marinković, Sladjana D.; Stanković, Miomir S. On \(q\)-orthogonal polynomials over a collection of complex origin intervals related to little \(q\)-Jacobi polynomials. (English) Zbl 1103.33009 Ramanujan J. 12, No. 2, 245-255 (2006). MSC: 33D45 42C05 × Cite Format Result Cite Review PDF Full Text: DOI
da Fonseca, C. M.; Petronilho, J. Explicit inverse of a tridiagonal \(k\)-Toeplitz matrix. (English) Zbl 1076.15011 Numer. Math. 100, No. 3, 457-482 (2005). Reviewer: Nicholas Karampetakis (Thessaloniki) MSC: 15A09 42C05 15B57 × Cite Format Result Cite Review PDF Full Text: DOI
Marcellán, F.; Petronilho, J. Eigenproblems for tridiagonal 2-Toeplitz matrices and quadratic polynomial mappings. (English) Zbl 0877.15010 Linear Algebra Appl. 260, 169-208 (1997). Reviewer: V.Burjan (Praha) MSC: 15A18 × Cite Format Result Cite Review PDF Full Text: DOI
Dette, Holger Characterizations of generalized Hermite and sieved ultraspherical polynomials. (English) Zbl 0863.33006 Trans. Am. Math. Soc. 348, No. 2, 691-711 (1996). Reviewer: P.A.McCoy (Annapolis) MSC: 33C45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Marcellán, Francisco; Sansigre, Gabriela Orthogonal polynomials and cubic transformations. (English) Zbl 0790.42010 J. Comput. Appl. Math. 49, No. 1-3, 161-168 (1993). MSC: 42C05 33C45 × Cite Format Result Cite Review PDF Full Text: DOI