Roberto S. Costas Santos graduated with a degree in Mathematical Sciences at the University of Seville in 1998, where he specialized in Measure Theory and Commutative Algebra. He obtained his PhD from the School of Engineering of the Carlos III University of Madrid in 2007, where he worked on the orthogonal polynomials and special functions theory with a unanimous grade of Outstanding Cum Laude. In 2007 he received a Fulbright scholarship from the Ministry of Science and Technology of the Government of Spain to continue his scientific training in the United States, and was hired by the College of William and Mary to be a visiting professor for one year. From 2010 to 2021, he worked as an interim professor at the University of Alcalá. He is currently a professor in the Department of Quantitative Methods, attached to the Faculty of Business Sciences at Loyola Andalucía University. He speaks and writes English (C1). Professor Costas has positive accreditation as a private university professor, assistant professor, and contracted professor by ANECA. He also has two six-year periods of research granted by ANECA. He also has been a full-time member of various research projects at Carlos III University in Madrid and innovation projects at the University of Alcalá where his group received an award as an innovative group. The results of my research activity can be summarized in a total of 42 scientific publications (mostly indexed in the Journal Citation Reports). His main interests can be divided into two blocks: the first (and main), focuses on the deep knowledge of the basic hypergeometric functions and their relationship with the classical orthogonal polynomials, always trying to extend known results; the second in the study of the irrationality of certain real numbers, the knowledge of properties of elementary symmetric functions and their relationship with linear algebra. In 2025 he published/edited with his coauthor Howard Saul Cohl his first book about q-series, and hypergeometric series.Throughout his professional career, he has directed various FTGs related to primary education and applied mathematics, has been a member of 11 TFG defense panels, has been a reviewer for Mathematical Reviews (153 items), ZbMATH (45 items), and has been a referee on more than 150 occasions for international journals. Profesor Costas has participated as well in more than 30 international conferences, where he has presented his work through lectures, and has given 29 seminars related to his two main areas of research. He is also member of American Mathematical Society and Real Sociedad Matemática Española.
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The Laguerre Constellation of Classical Orthogonal Polynomials COSTAS SANTOS, ROBERTO SANTIAGO 01/01/2025 Article |
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Investigating Multidimensional Degenerate Hybrid Special Polynomials and Their Connection to Appell Sequences: Properties and Applications Alqahtani, Awatif Muflih , Yousuf, Saleem , Wani, Shahid Ahmad , COSTAS SANTOS, ROBERTO SANTIAGO 01/12/2024 Article |
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On Polar Jacobi Polynomials COSTAS SANTOS, ROBERTO SANTIAGO 01/09/2024 Article |
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LOCALIZATION OF ZEROS OF POLAR POLYNOMIALS ON THE UNIT DISK COSTAS SANTOS, ROBERTO SANTIAGO, Rehouma, Abdelhamid 01/08/2024 Article |
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Multi-integral representations for Jacobi functions of the first and second kind Cohl H.S. , COSTAS SANTOS, ROBERTO SANTIAGO 13/12/2023 Article |
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Integral Representations of a Generalized Linear Hermite Functional COSTAS SANTOS, ROBERTO SANTIAGO 01/07/2023 Article |
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Nonterminating transformations and summations associated with some q-Mellin–Barnes integrals Cohl H.S. , COSTAS SANTOS, ROBERTO SANTIAGO 01/06/2023 Article |
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Symmetry of terminating basic hypergeometric series representations of the Askey–Wilson polynomials Cohl H.S. , COSTAS SANTOS, ROBERTO SANTIAGO 01/01/2023 Article |
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Generalizations of generating functions for basic hypergeometric orthogonal polynomials Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO, Hwang, Philbert R. , Wakhare, Tanay V. 19/11/2022 Article |
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On the Relation Between Gegenbauer Polynomials and the Ferrers Function of the First Kind Cohl, H. S. , COSTAS SANTOS, ROBERTO SANTIAGO 01/09/2022 Article |
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Utility of integral representations for basic hypergeometric functions and orthogonal polynomials Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO 23/06/2022 Article |
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On Polynomials Orthogonal with Respect to an Inner Product Involving Higher-Order Differences: The Meixner Case COSTAS SANTOS, ROBERTO SANTIAGO, Soria-Lorente, Anier , Vilaire, Jean-Marie 01/06/2022 Article |
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Multi-Integral Representations for Associated Legendre and Ferrers Functions Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO 01/10/2020 Article |
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Terminating Basic Hypergeometric Representations and Transformations for the Askey-Wilson Polynomials Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO, Ge, Linus 01/08/2020 Article |
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On a generalization of the Rogers generating function Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO, Wakhare, Tanay V. 15/07/2019 Article |
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Some Generating Functions for q-Polynomials Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO, Wakhare, Tanay V. 01/12/2018 Article |
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Analytic properties of some basic hypergeometric-Sobolev-type orthogonal polynomials COSTAS SANTOS, ROBERTO SANTIAGO, Soria-Lorente, Anier 02/11/2018 Article |
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The power collection method for connection relations: Meixner polynomials Badder, H. S. , Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO, Xu, William 08/11/2017 Article |
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Matrices totally positive relative to a tree, II COSTAS SANTOS, ROBERTO SANTIAGO, Johnson, C. R. 15/09/2016 Article |
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THE COMPLEMENTARY POLYNOMIALS AND THE RODRIGUES OPERATOR OF CLASSICAL ORTHOGONAL POLYNOMIALS COSTAS SANTOS, ROBERTO SANTIAGO, Marcellan Espanol, Francisco 01/10/2012 Article |
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Zeros of polynomials orthogonal with respect to a signed weight Atia, M. J. , Benabdallah, M. , COSTAS SANTOS, ROBERTO SANTIAGO 01/03/2012 Article |
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Orthogonality of q-polynomials for non-standard parameters COSTAS SANTOS, ROBERTO SANTIAGO, Sanchez-Lara, J. F. 01/09/2011 Article |
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The semiclassical Sobolev orthogonal polynomials A general approach COSTAS SANTOS, ROBERTO SANTIAGO, Moreno-Balcazar, J. J. 01/01/2011 Article |
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q-Classical Orthogonal Polynomials: A General Difference Calculus Approach COSTAS SANTOS, ROBERTO SANTIAGO, Marcellan, F. 01/07/2010 Article |
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On the elementary symmetric functions of a sum of matrices COSTAS SANTOS, ROBERTO SANTIAGO 24/08/2009 Article |
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MATRICES TOTALLY POSITIVE RELATIVE TO A TREE Johnson, Charles R. , COSTAS SANTOS, ROBERTO SANTIAGO, Tadchiev, Boris 01/04/2009 Article |
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Extensions of discrete classical orthogonal polynomials beyond the orthogonality COSTAS SANTOS, ROBERTO SANTIAGO, Sanchez-Lara, J. F. 15/03/2009 Article |
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Second structure relation for q-semiclassical polynomials of the Hahn Tableau COSTAS SANTOS, ROBERTO SANTIAGO, Marcellan, F. 01/05/2007 Article |
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Factorization of the hypergeometric-type difference equation on the uniform lattice Alvarez-Nodarse, R. , Atakishiyev, N. M. , COSTAS SANTOS, ROBERTO SANTIAGO 01/01/2007 Article |
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Limit relations between q-Krall type orthogonal polynomials Alvarez-Nodarse, R. , COSTAS SANTOS, ROBERTO SANTIAGO 01/10/2006 Article |
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A q-analog of Racah polynomials and q-algebra SUq(2) in quantum optics Alvarez-Nodarse, R. , Smirnov, Yu. F. , COSTAS SANTOS, ROBERTO SANTIAGO 01/01/2006 Article |
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Factorization of the hypergeometric-type difference equation on non-uniform lattices: dynamical algebra Alvarez-Nodarse, R , Atakishiyev, NM , COSTAS SANTOS, ROBERTO SANTIAGO 07/01/2005 Article |
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Principal minor sums of (A+tB)^m Johnson, Charles , Leichenauer, Stefan , McNamara, Peter , COSTAS SANTOS, ROBERTO SANTIAGO 01/01/2005 Article |
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Factorization method for difference equations of hypergeometric type on nonuniform lattices Alvarez-Nodarse, R , COSTAS SANTOS, ROBERTO SANTIAGO 13/07/2001 Article |
| Congresses |
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Orthogonality of the big -1 Jacobi polynomials for non-standard parameters Cohl, H.S. , COSTAS SANTOS, ROBERTO SANTIAGO 01/01/2025 Conference Paper |
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Double summation addition theorems for Jacobi functions of the ?rst and second kind Cohl, H.S. , COSTAS SANTOS, ROBERTO SANTIAGO, Durand, L. , Montoya, C. , Olafsson, G. 01/01/2025 Conference Paper |
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Multi-integral representations for Jacobi functions of the first and second kind COSTAS SANTOS, ROBERTO SANTIAGO 15/07/2024 - 19/07/2024 Ponencia del Congreso |
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Sobolev orthogonal polynomials: connection formulas and zeros COSTAS SANTOS, ROBERTO SANTIAGO 24/06/2024 - 28/06/2024 Ponencia del Congreso |
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Orthogonality of the big -1 Jacobi polynomials for non-standard parameters Cohl, Howard S , COSTAS SANTOS, ROBERTO SANTIAGO 01/03/2023 - 03/03/2023 Ponencia del Congreso |
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Hypergeometric functions, difference equations and Wronskians. COSTAS SANTOS, ROBERTO SANTIAGO 12/07/2022 - 17/07/2022 Ponencia del Congreso |
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Una sesión básica de Latex COSTAS SANTOS, ROBERTO SANTIAGO 27/01/2022 - 27/01/2022 Ponencia del Congreso |
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Multi-integral representations for associated Legendre and Ferrers functions Cohl, Howard S , COSTAS SANTOS, ROBERTO SANTIAGO 02/12/2021 - 07/12/2021 Ponencia del Congreso |
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Classical Orthogonal Polynomials: Orthogonality and duality COSTAS SANTOS, ROBERTO SANTIAGO 01/09/2019 - 07/09/2019 Ponencia del Congreso |
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Exceptional Orthogonal Polynomials from the Semi-classical point of view COSTAS SANTOS, ROBERTO SANTIAGO 21/07/2019 - 26/09/2019 Ponencia del Congreso |
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A first study of Zeros of Classical Orthogonal Polynomial COSTAS SANTOS, ROBERTO SANTIAGO 08/03/2018 - 08/03/2018 Ponencia del Congreso |
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q-Polynomials for non-standard parameters. Orthogonality and new identities COSTAS SANTOS, ROBERTO SANTIAGO 03/07/2017 - 07/07/2017 Ponencia del Congreso |
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Basic hypergeometric orthogonal polynomials COSTAS SANTOS, ROBERTO SANTIAGO 16/02/2016 Ponencia del Congreso |
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q-polynomials. Orthogonality in the complex plane and more COSTAS SANTOS, ROBERTO SANTIAGO 26/08/2015 - 29/08/2015 Ponencia del Congreso |
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Conociendo mejor a los q-polinomios COSTAS SANTOS, ROBERTO SANTIAGO 08/06/2015 - 12/06/2015 Ponencia del Congreso |
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Generalizations of Generating Functions for Meixner and Krawtchouk Polynomials COSTAS SANTOS, ROBERTO SANTIAGO 01/06/2015 - 05/06/2015 Ponencia del Congreso |
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Extensions of discrete orthogonal polynomials beyond the orthogonality COSTAS SANTOS, ROBERTO SANTIAGO 10/05/2015 - 12/05/2015 Ponencia del Congreso |
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La función Zeta de Riemann y sus q-extensiones. Aplicaciones COSTAS SANTOS, ROBERTO SANTIAGO 05/03/2015 - 05/03/2015 Ponencia del Congreso |
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Segunda relación de estructura para q-polinomios clásicos y semiclásicos COSTAS SANTOS, ROBERTO SANTIAGO 05/03/2015 - 05/03/2015 Ponencia del Congreso |
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Recent results on classical orthogonal polynomials COSTAS SANTOS, ROBERTO SANTIAGO 05/03/2015 - 05/03/2015 Ponencia del Congreso |
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Orthogonality of q-polynomials for nonstandard parameters COSTAS SANTOS, ROBERTO SANTIAGO 05/03/2015 - 05/03/2015 Ponencia del Congreso |
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Classical orthogonal polynomials beyond the classical parameters COSTAS SANTOS, ROBERTO SANTIAGO 05/03/2015 - 05/03/2015 Ponencia del Congreso |
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The orthogonality relations of the Al-Salam-Carlitz polynomials for general parameters COSTAS SANTOS, ROBERTO SANTIAGO 05/03/2015 - 05/03/2015 Ponencia del Congreso |
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Matrices totally positive relative to a tree COSTAS SANTOS, ROBERTO SANTIAGO 05/03/2015 - 05/03/2015 Ponencia del Congreso |
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Exceptional Orthogonal Polynomials from the Semi-classical point of view COSTAS SANTOS, ROBERTO SANTIAGO 05/03/2015 - 05/03/2015 Ponencia del Congreso |
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Sobre algunas propiedades de la función Zeta de Riemann COSTAS SANTOS, ROBERTO SANTIAGO 05/03/2015 - 05/03/2015 Ponencia del Congreso |
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El operador de Rodrigues y los polinomios multi-ortogonales de tipo II COSTAS SANTOS, ROBERTO SANTIAGO 05/03/2015 - 05/03/2015 Ponencia del Congreso |
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Curso basico de PROSPER COSTAS SANTOS, ROBERTO SANTIAGO 05/03/2015 - 05/03/2015 Ponencia del Congreso |
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El método de factorización para ecuaciones en diferencias de tipo hipergeométrico COSTAS SANTOS, ROBERTO SANTIAGO 05/03/2015 - 05/03/2015 Ponencia del Congreso |
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El método de factorización de ecuaciones en diferencias de tipo hipergeométrico sobre redes no lineales COSTAS SANTOS, ROBERTO SANTIAGO 05/03/2015 - 05/03/2015 Ponencia del Congreso |
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Método de Factorización de ecuaciones en diferencias de tipo hipergeométrico en redes no uniformes COSTAS SANTOS, ROBERTO SANTIAGO 05/03/2015 - 05/03/2015 Ponencia del Congreso |
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An overview of Classical Orthogonal Polynomials COSTAS SANTOS, ROBERTO SANTIAGO 25/03/2014 - 25/03/2014 Ponencia del Congreso |
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Discovering Discrete Classical Polynomials: First Steps COSTAS SANTOS, ROBERTO SANTIAGO 25/03/2014 - 25/03/2014 Ponencia del Congreso |
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A connection between the legendre polynomials and the Riemann Zeta function. II COSTAS SANTOS, ROBERTO SANTIAGO 16/09/2013 - 20/09/2013 Ponencia del Congreso |
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A connection between the Legendre polynomials and the Riemann Zeta function. I COSTAS SANTOS, ROBERTO SANTIAGO 28/08/2013 - 30/08/2013 Ponencia del Congreso |
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Multiple Meixner polynomials of second type with non-classical parameters. A first study. COSTAS SANTOS, ROBERTO SANTIAGO 24/03/2013 - 29/03/2013 Ponencia del Congreso |
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Los polinomios ortogonales clásicos y de Sobolev: viejos y nuevos resultados COSTAS SANTOS, ROBERTO SANTIAGO 28/02/2012 - 28/02/2012 Ponencia del Congreso |
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Old and new results on Sobolev and semi-classical orthogonal polynomials. COSTAS SANTOS, ROBERTO SANTIAGO 21/08/2011 - 02/09/2011 Ponencia del Congreso |
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On a degenerative version of the Favard’s theorem COSTAS SANTOS, ROBERTO SANTIAGO 26/06/2010 - 30/06/2010 Ponencia del Congreso |
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Extensions of discrete classical orthogonal polynomials beyond the orthogonality. COSTAS SANTOS, ROBERTO SANTIAGO 20/07/2009 - 25/07/2009 Ponencia del Congreso |
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On the determinant of a sum of matrices. COSTAS SANTOS, ROBERTO SANTIAGO 01/10/2008 Ponencia del Congreso |
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The semiclassical-Sobolev polynomials. A general approach. Moreno Balcazar, Juan José , COSTAS SANTOS, ROBERTO SANTIAGO 01/09/2008 Ponencia del Congreso |
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Algunas propiedades algebraicas de la función Zeta de Riemann COSTAS SANTOS, ROBERTO SANTIAGO 21/05/2007 - 21/05/2007 Ponencia del Congreso |
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Classical orthogonal polynomials. A general difference calculus approach COSTAS SANTOS, ROBERTO SANTIAGO 01/08/2006 Ponencia del Congreso |
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Limit relations between q-Krall type orthogonal polynomials COSTAS SANTOS, ROBERTO SANTIAGO 01/07/2006 Ponencia del Congreso |
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Limit relations between q-Krall type orthogonal polynomials COSTAS SANTOS, ROBERTO SANTIAGO 01/03/2006 Ponencia del Congreso |
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Factorization of the hypergeometric-type difference equations on non-uniform lattices: dynamical algebra. COSTAS SANTOS, ROBERTO SANTIAGO 01/07/2005 Ponencia del Congreso |
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Number Theory, q-calculus. The zeta and q-zeta functions. COSTAS SANTOS, ROBERTO SANTIAGO 01/07/2004 Ponencia del Congreso |
| Book chapters and books |
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Applications and q-Extensions of Hypergeometric Functions 01/01/2025 Libro Completo |
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Classical hypergeometric functions and generalizations 01/01/2025 Libro Completo |
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Double summation addition theorems for Jacobi functions of the first and second kind 01/01/2025 Capítulo de un Libro |
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Sobolev orthogonal polynomials: Connection formulae 23/12/2022 Capítulo de un Libro |
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Actas del XIII Congreso de Tecnología, Aprendizaje y Enseñanza de la Electrónica 22/06/2018 Capítulo de un Libro |
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The orthogonality of Al-Salam-Carlitz polynomials for complex parameters 01/01/2018 Capítulo de un Libro |
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ATICA 2016. Aplicaciones de Tecnologías de la Información y Comunicaciones Avanzadas. 09/11/2016 Capítulo de un Libro |
| External Projects |
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Contrato de trabajo de duración determinada. Convocatoria de ayudas de la investigación posdoctoral del Ministerio de Educación y Ciencia. Project start date: 30/04/2008 |