Publications
Publications as Editor
- M.N. Rebocho and N. Witte, (2023). Integrable Differential Systems for Deformed Laguerre-Hahn Orthogonal Polynomials. Nonlinearity 36, no. 7, 3542.
- Y. Chen, G. Filipuk, and M.N. Rebocho, A system of nonlinear difference equations for recurrence relation coefficients of a modified Jacobi weight, Contemporary Mathematics, Vol. 782, 2023 (8 pp.)
- M.N. Rebocho, Divided-difference operators from the geometric point of view, Formal and analytic solutions of differential equations, 301–324, World Sci. Publ., Hackensack, NJ, 2022.
- M.N. Rebocho, On the second order holonomic equation for Sobolev-type orthogonal polynomials, Appl. Anal. 101, no. 1 (2022) 314–336.
- G. Filipuk and M.N. Rebocho, The symmetric semi-classical orthogonal polynomials of class two and some of their extensions, Bull. Malays. Math. Sci. Soc. 43, no. 3 (2020) 2235-2253.
- G. Filipuk and M.N. Rebocho, Classification of Laguerre-Hahn orthogonal polynomials of class one, Math. Nachr. 293, no. 2 (2020) 244-262.
- M.N. Rebocho, Laguerre-Hahn orthogonal polynomials on the real line, Random Matrices Theory Appl. 9, no. 1 (2020) 2040001 (33 pages).
- Y. Chen, G. Filipuk, and M.N. Rebocho, Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics, Jaen J. Approx. 11 (1-2) (2019) 47-65.
- G. Filipuk and M.N. Rebocho, Discrete semi-classical orthogonal polynomials of class one on quadratic lattices, J. Difference Equ. Appl. 25 (2019) 1–20.
- G. Filipuk and M.N. Rebocho, Symmetric semi-classical orthogonal polynomials of class one on q-quadratic lattices, Formal and analytic solutions of diff. equations, 251-–261, Springer Proc. Math. Stat., 256, Springer, Cham, 2018.
- A. Branquinho, Y. Chen, G. Filipuk, and M.N. Rebocho, A characterization theorem for semi-classical orthogonal polynomials on non-uniform lattices, Appl. Math. Comput. 334 (2018) 356-366.
- G. Filipuk and M.N. Rebocho, Differential equations for families of semi-classical orthogonal polynomials within class one, Appl. Numer. Math. 124
(2018) 76-88. - K. Castillo and M.N. Rebocho, On linear spectral transformations and the Laguerre-Hahn class, Integral Transforms Spec. Funct. 28 (2017) 859-875.
- G. Filipuk and M.N. Rebocho, Orthogonal polynomials on systems of non-uniform lattices from compatibility conditions, J. Math. Anal. Appl. 456
(2017) 1380-1396. - G. Filipuk and M.N. Rebocho, Discrete Painlevé Equations for Recurrence Coefficients of Laguerre-Hahn Orthogonal Polynomials of Class One , Integral Transforms Spec. Funct. 27 (2016) 548-565.
- K. Castillo, F. Marcellan, and M.N. Rebocho, Zeros of para-orthogonal polynomials and linear spectral transformations on the unit circle , Numer. Algor. 71 (2016) 699-714.
- M.N. Rebocho, On Laguerre-Hahn affine orthogonal polynomials on the unit circle from matrix Sylvester equations , Integral Transforms Spec. Funct. 27 (2016) 78-93.
- A. Branquinho, A. Foulquie Moreno, A. Paiva, and M.N. Rebocho, Second-order differential equations in the Laguerre-Hahn class, Appl. Numer. Math. 94 (2015) 16-32.
- A. Branquinho and M.N. Rebocho, Characterization theorem for Laguerre-Hahn orthogonal polynomials on non-uniform lattices, J. Math. Anal. Appl. 427 (2015) 185 - 201.
- A. Branquinho and M.N. Rebocho, Deformed Laguerre-Hahn orthogonal polynomials on the real line, Appl. Math. Comput. 233 (2014) 359-368.
- A. Branquinho, A. Paiva, and M.N. Rebocho, Sylvester equations for Laguerre-Hahn orthogonal polynomials on the real line , Appl. Math. Comput. 219 (17) (2013) 9118-9131.
- A. Branquinho and M.N. Rebocho, Structure relations for orthogonal polynomials on the unit circle , Linear Alg. Appl. 436 (11) (2012) 4296-4310.
- A. Branquinho and M.N. Rebocho, On the semiclassical character of orthogonal polynomials satisfying structure relations , J. Diference Equ. Appl. 18 (1) (2012) 111-138.
- A. Branquinho and M.N. Rebocho, Difference and differential equations for deformed Laguerre-Hahn orthogonal polynomials on the unit circle , J. Phys. A: Math. Theor. 44 (46) (2011) 465204.
- A. Branquinho and M.N. Rebocho, Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle , Bull. Belg. Math. Soc. Simon Stevin 17 (2) (2010) 355-376.
- A. Branquinho and M.N. Rebocho, Distributional equation for Laguerre-Hahn functionals on the unit circle , J. Comput. Appl. Math. 233 (3) (2009) 634-642.
- A. Branquinho and M.N. Rebocho, On differential equations for orthogonal polynomials on the unit circle, J. Math. Anal. Appl. 356 (1) (2009) 242-256.
- A. Branquinho, A. Foulquie Moreno, F. Marcellan, and M.N. Rebocho, Coherent pairs of linear functionals on the unit circle , J. Approx. Theory 153 (1) (2008) 122-137.
- A. Branquinho and M.N. Rebocho, Characterizations of Laguerre-Hahn afne orthogonal polynomials on the unit circle , J. Comput. Anal. Appl. 10 (2) (2008) 229-242.
- Polinómios ortogonais do tipo Laguerre-Hahn sobre a circunferência unitária, PhD dissertation, University of Coimbra, 2008.
- Problemas de momentos e polinómios ortogonais , Master dissertation, University of Coimbra, 2001.
Publications as Editor
- Complex ODEs: asymptotics, orthogonal polynomials and random matrices. Random Matrices Theory Appl. 9 (2020), no. 1 (Y. Chen, G. Filipuk, M.N. Rebocho, and D. Sauzin, Eds.)
- Random matrices, Painlevé equations, integrable systems in orthogonal polynomials and related topics—Part I. Random Matrices Theory Appl. 6 (2017), no. 4 (Y. Chen, G. Filipuk, and M.N. Rebocho, Eds.)
- Special issue: Random matrices, Painlevé equations, integrable systems in orthogonal polynomials and related topics—Part II. Random Matrices Theory Appl. 7 (2018), no. 4.
(Y. Chen, G. Filipuk, and M.N. Rebocho, Eds.)
Communications in international meetings
Other communications
- Workshop on Integrable Systems and Orthogonal Polynomials - Numerical and Analytical Perspectives, 2023, Cape Town, South Africa
- Functional Analysis, Approximation Theory and Numerical Analysis (FAATNA 20>22), 2022, Matera, Italy
- 16th International Symposium on Orthogonal Polynomials, Special Functions and Applications, 2022 (Online)
- International Conference on Orthogonal Polynomials Celebrating Francisco Marcellán's 70th birthday, 2022, Cádiz, Spain
- Formal and Analytic Solutions of Diff. Equations on the Internet (FASnet20), 2020 (Online)
- VI Workshop on Computational Data Analysis and Numerical Methods, 2019, Covilhã, Portugal
- WSMC12 - 12th Workshop on Statistics, Mathematics and Computation, 2018, Covilhã, Portugal
- 32nd International Colloquium on Group Theoretical Methods in Physics (Group32), 2018, Prague, Czech Republic
- Eibpoa 2018, VII Encuentro Iberoamericano de Polinomios Ortogonales y sus Aplicaciones, 2018, Madrid, Spain
- FASdiff17, Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential,...), 2017, Alcalá de Henares, Spain
- XII International Conference Approximation and Optimization in the Caribbean, 2016, Havana, Cuba
- The Real World is Complex, An international Symposium in honor of Christian Berg, 2015, Copenhagen, Denmark
- Progress on difference equations- PODE 2015, Covilhã, Portugal
- I Congresso Brasileiro de Jovens Pesquisadores em Matemática Pura e Aplicada, 2014, São Paulo, Brazil
- V Jaen Conference on Approximation, 2014, Úbeda, Spain
- Statistics and Mathematical Sciences Workshop - SMSW'14, Covilhã, Portugal
- OrthoQuad 2014 In memory of Pablo González Vera, 2014, Tenerife, Spain
- 12th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA12), 2013, Sousse, Tunisia
- International conference on differential equations, difference equations and special functions (ICDDESF), 2012, Patras, Greece
- 11th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA11), 2011, Madrid, Spain
- Special Functions in the 21st Century: Theory and Applications, 2011, Washington DC, USA
- Congreso de la Real Sociedad Matemática Española 2011, Ávila, Spain
- Workshop on Integral Transforms Positivity and Applications 2010, Copenhagen, Denmark
- I Jaen Conference on Approximation 2010, Úbeda, Spain
- 10th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA10), 2009, Leuven, Belgium
- Computational Methods and Function Theory 09 (CMFT 09), Ankara, Turkey
- 11th European Workshop on Applications and Generalizations of Complex Analysis, 2009, Coimbra, Portugal
- IWOPA'08 Conference in honor of Guillermo López Lagomasino's 60th birthday, 2008, Madrid, Spain
- 10th Annual Workshop on Applications and Generalizations of Complex Analysis, 2007, Coimbra, Portugal
- 9th European Workshop on Applications and Generalizations of Complex Analysis, 2006, Coimbra, Portugal
- 8th Annual Workshop on Applications and Generalizations of Complex Analysis, 2005, Aveiro, Portugal
- Summer School on Orthogonal Polynomials and Special Functions: Approximation and Iteration, 2003, Coimbra, Portugal
- 4th Annual Workshop on Applications and Generalizations of Complex Analysis, 2001, Coimbra, Portugal
Other communications
- Deformed orthogonal polynomials on the real line, 13/04/2023, Seminário do Grupo de Análise Funcional e Aplicações (GAFA) do CIDMA/DMat-UA, Univ. Aveiro.
- Deformed orthogonal polynomials on the real line, 16/12/2022, Seminários TAPO - Teoría de aproximación y polinomios ortogonales, Departamento de Matemáticas, Univ. Almeria
- On the direct problem for Laguerre-Hahn orthogonal polynomials on the real line, 15/03/2019, Univ. Aveiro
- On discrete semi-classical orthogonal polynomials on non-uniform lattices, 20/12/2018, UC3M, Madrid
- Old and new results on discrete semi-classical Orthogonal Polynomials on systems of non-uniform lattices, 18/01/2018, TU Dresden
- On discrete semi-classical orthogonal polynomials on non-uniform lattices, 12/04/2017, Univ. Macau
- On discrete Painlevé Equations for Recurrence Coefficients of Laguerre-Hahn Orthogonal Polynomials, 10/03/2017, Univ. Warsaw
- On classical orthogonal polynomials and some of their extensions via Sylvester equations, 13/01/2015, ISCTE-IUL
- Deformed Laguerre-Hahn orthogonal polynomials on the real line, 19/06/2014, Department of Mathematics - UBI
- Sylvester equations for Laguerre-Hahn orthogonal polynomials on the real line, 12/04/2013, CMUC
- Laguerre-Hahn orthogonal polynomials on the unit circle, 02/11/2010, Department of Mathematics - TU Berlin
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