LOYOLA
Research

Scientific offer
and research groups


ROBERTO SANTIAGO COSTAS SANTOS

ROBERTO SANTIAGO COSTAS SANTOS

Category: Assistant Professor/Tenure Track
Area of knowledge: Not available
ORCID iD: 0000-0002-9545-7411
Research Unit: Métodos de Investigación Cuantitativa y aplicaciones (MICA)
AACSB
Quantitative Methods

Publications

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.

Articles or Reviews

Publications
The Laguerre Constellation of Classical Orthogonal Polynomials
COSTAS SANTOS, ROBERTO SANTIAGO
01/01/2025
Article
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
On Polar Jacobi Polynomials
COSTAS SANTOS, ROBERTO SANTIAGO
01/09/2024
Article
LOCALIZATION OF ZEROS OF POLAR POLYNOMIALS ON THE UNIT DISK
COSTAS SANTOS, ROBERTO SANTIAGO, Rehouma, Abdelhamid
01/08/2024
Article
Multi-integral representations for Jacobi functions of the first and second kind
Cohl H.S. , COSTAS SANTOS, ROBERTO SANTIAGO
13/12/2023
Article
Integral Representations of a Generalized Linear Hermite Functional
COSTAS SANTOS, ROBERTO SANTIAGO
01/07/2023
Article
Nonterminating transformations and summations associated with some q-Mellin–Barnes integrals
Cohl H.S. , COSTAS SANTOS, ROBERTO SANTIAGO
01/06/2023
Article
Symmetry of terminating basic hypergeometric series representations of the Askey–Wilson polynomials
Cohl H.S. , COSTAS SANTOS, ROBERTO SANTIAGO
01/01/2023
Article
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
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
Utility of integral representations for basic hypergeometric functions and orthogonal polynomials
Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO
23/06/2022
Article
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
Multi-Integral Representations for Associated Legendre and Ferrers Functions
Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO
01/10/2020
Article
Terminating Basic Hypergeometric Representations and Transformations for the Askey-Wilson Polynomials
Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO, Ge, Linus
01/08/2020
Article
On a generalization of the Rogers generating function
Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO, Wakhare, Tanay V.
15/07/2019
Article
Some Generating Functions for q-Polynomials
Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO, Wakhare, Tanay V.
01/12/2018
Article
Analytic properties of some basic hypergeometric-Sobolev-type orthogonal polynomials
COSTAS SANTOS, ROBERTO SANTIAGO, Soria-Lorente, Anier
02/11/2018
Article
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
Matrices totally positive relative to a tree, II
COSTAS SANTOS, ROBERTO SANTIAGO, Johnson, C. R.
15/09/2016
Article
THE COMPLEMENTARY POLYNOMIALS AND THE RODRIGUES OPERATOR OF CLASSICAL ORTHOGONAL POLYNOMIALS
COSTAS SANTOS, ROBERTO SANTIAGO, Marcellan Espanol, Francisco
01/10/2012
Article
Zeros of polynomials orthogonal with respect to a signed weight
Atia, M. J. , Benabdallah, M. , COSTAS SANTOS, ROBERTO SANTIAGO
01/03/2012
Article
Orthogonality of q-polynomials for non-standard parameters
COSTAS SANTOS, ROBERTO SANTIAGO, Sanchez-Lara, J. F.
01/09/2011
Article
The semiclassical Sobolev orthogonal polynomials A general approach
COSTAS SANTOS, ROBERTO SANTIAGO, Moreno-Balcazar, J. J.
01/01/2011
Article
q-Classical Orthogonal Polynomials: A General Difference Calculus Approach
COSTAS SANTOS, ROBERTO SANTIAGO, Marcellan, F.
01/07/2010
Article
On the elementary symmetric functions of a sum of matrices
COSTAS SANTOS, ROBERTO SANTIAGO
24/08/2009
Article
MATRICES TOTALLY POSITIVE RELATIVE TO A TREE
Johnson, Charles R. , COSTAS SANTOS, ROBERTO SANTIAGO, Tadchiev, Boris
01/04/2009
Article
Extensions of discrete classical orthogonal polynomials beyond the orthogonality
COSTAS SANTOS, ROBERTO SANTIAGO, Sanchez-Lara, J. F.
15/03/2009
Article
Second structure relation for q-semiclassical polynomials of the Hahn Tableau
COSTAS SANTOS, ROBERTO SANTIAGO, Marcellan, F.
01/05/2007
Article
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
Limit relations between q-Krall type orthogonal polynomials
Alvarez-Nodarse, R. , COSTAS SANTOS, ROBERTO SANTIAGO
01/10/2006
Article
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
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
Principal minor sums of (A+tB)^m
Johnson, Charles , Leichenauer, Stefan , McNamara, Peter , COSTAS SANTOS, ROBERTO SANTIAGO
01/01/2005
Article
Factorization method for difference equations of hypergeometric type on nonuniform lattices
Alvarez-Nodarse, R , COSTAS SANTOS, ROBERTO SANTIAGO
13/07/2001
Article

Conference Paper, Proceedings Paper, Conference Presentation or Abstract

Congresses
Orthogonality of the big -1 Jacobi polynomials for non-standard parameters
Cohl, H.S. , COSTAS SANTOS, ROBERTO SANTIAGO
01/01/2025
Conference Paper
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
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
Sobolev orthogonal polynomials: connection formulas and zeros
COSTAS SANTOS, ROBERTO SANTIAGO
24/06/2024 - 28/06/2024
Ponencia del Congreso
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
Hypergeometric functions, difference equations and Wronskians.
COSTAS SANTOS, ROBERTO SANTIAGO
12/07/2022 - 17/07/2022
Ponencia del Congreso
Una sesión básica de Latex
COSTAS SANTOS, ROBERTO SANTIAGO
27/01/2022 - 27/01/2022
Ponencia del Congreso
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
Classical Orthogonal Polynomials: Orthogonality and duality
COSTAS SANTOS, ROBERTO SANTIAGO
01/09/2019 - 07/09/2019
Ponencia del Congreso
Exceptional Orthogonal Polynomials from the Semi-classical point of view
COSTAS SANTOS, ROBERTO SANTIAGO
21/07/2019 - 26/09/2019
Ponencia del Congreso
A first study of Zeros of Classical Orthogonal Polynomial
COSTAS SANTOS, ROBERTO SANTIAGO
08/03/2018 - 08/03/2018
Ponencia del Congreso
q-Polynomials for non-standard parameters. Orthogonality and new identities
COSTAS SANTOS, ROBERTO SANTIAGO
03/07/2017 - 07/07/2017
Ponencia del Congreso
Basic hypergeometric orthogonal polynomials
COSTAS SANTOS, ROBERTO SANTIAGO
16/02/2016
Ponencia del Congreso
q-polynomials. Orthogonality in the complex plane and more
COSTAS SANTOS, ROBERTO SANTIAGO
26/08/2015 - 29/08/2015
Ponencia del Congreso
Conociendo mejor a los q-polinomios
COSTAS SANTOS, ROBERTO SANTIAGO
08/06/2015 - 12/06/2015
Ponencia del Congreso
Generalizations of Generating Functions for Meixner and Krawtchouk Polynomials
COSTAS SANTOS, ROBERTO SANTIAGO
01/06/2015 - 05/06/2015
Ponencia del Congreso
Extensions of discrete orthogonal polynomials beyond the orthogonality
COSTAS SANTOS, ROBERTO SANTIAGO
10/05/2015 - 12/05/2015
Ponencia del Congreso
La función Zeta de Riemann y sus q-extensiones. Aplicaciones
COSTAS SANTOS, ROBERTO SANTIAGO
05/03/2015 - 05/03/2015
Ponencia del Congreso
Segunda relación de estructura para q-polinomios clásicos y semiclásicos
COSTAS SANTOS, ROBERTO SANTIAGO
05/03/2015 - 05/03/2015
Ponencia del Congreso
Recent results on classical orthogonal polynomials
COSTAS SANTOS, ROBERTO SANTIAGO
05/03/2015 - 05/03/2015
Ponencia del Congreso
Orthogonality of q-polynomials for nonstandard parameters
COSTAS SANTOS, ROBERTO SANTIAGO
05/03/2015 - 05/03/2015
Ponencia del Congreso
Classical orthogonal polynomials beyond the classical parameters
COSTAS SANTOS, ROBERTO SANTIAGO
05/03/2015 - 05/03/2015
Ponencia del Congreso
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
Matrices totally positive relative to a tree
COSTAS SANTOS, ROBERTO SANTIAGO
05/03/2015 - 05/03/2015
Ponencia del Congreso
Exceptional Orthogonal Polynomials from the Semi-classical point of view
COSTAS SANTOS, ROBERTO SANTIAGO
05/03/2015 - 05/03/2015
Ponencia del Congreso
Sobre algunas propiedades de la función Zeta de Riemann
COSTAS SANTOS, ROBERTO SANTIAGO
05/03/2015 - 05/03/2015
Ponencia del Congreso
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
Curso basico de PROSPER
COSTAS SANTOS, ROBERTO SANTIAGO
05/03/2015 - 05/03/2015
Ponencia del Congreso
El método de factorización para ecuaciones en diferencias de tipo hipergeométrico
COSTAS SANTOS, ROBERTO SANTIAGO
05/03/2015 - 05/03/2015
Ponencia del Congreso
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
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
An overview of Classical Orthogonal Polynomials
COSTAS SANTOS, ROBERTO SANTIAGO
25/03/2014 - 25/03/2014
Ponencia del Congreso
Discovering Discrete Classical Polynomials: First Steps
COSTAS SANTOS, ROBERTO SANTIAGO
25/03/2014 - 25/03/2014
Ponencia del Congreso
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
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
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
Los polinomios ortogonales clásicos y de Sobolev: viejos y nuevos resultados
COSTAS SANTOS, ROBERTO SANTIAGO
28/02/2012 - 28/02/2012
Ponencia del Congreso
Old and new results on Sobolev and semi-classical orthogonal polynomials.
COSTAS SANTOS, ROBERTO SANTIAGO
21/08/2011 - 02/09/2011
Ponencia del Congreso
On a degenerative version of the Favard’s theorem
COSTAS SANTOS, ROBERTO SANTIAGO
26/06/2010 - 30/06/2010
Ponencia del Congreso
Extensions of discrete classical orthogonal polynomials beyond the orthogonality.
COSTAS SANTOS, ROBERTO SANTIAGO
20/07/2009 - 25/07/2009
Ponencia del Congreso
On the determinant of a sum of matrices.
COSTAS SANTOS, ROBERTO SANTIAGO
01/10/2008
Ponencia del Congreso
The semiclassical-Sobolev polynomials. A general approach.
Moreno Balcazar, Juan José , COSTAS SANTOS, ROBERTO SANTIAGO
01/09/2008
Ponencia del Congreso
Algunas propiedades algebraicas de la función Zeta de Riemann
COSTAS SANTOS, ROBERTO SANTIAGO
21/05/2007 - 21/05/2007
Ponencia del Congreso
Classical orthogonal polynomials. A general difference calculus approach
COSTAS SANTOS, ROBERTO SANTIAGO
01/08/2006
Ponencia del Congreso
Limit relations between q-Krall type orthogonal polynomials
COSTAS SANTOS, ROBERTO SANTIAGO
01/07/2006
Ponencia del Congreso
Limit relations between q-Krall type orthogonal polynomials
COSTAS SANTOS, ROBERTO SANTIAGO
01/03/2006
Ponencia del Congreso
Factorization of the hypergeometric-type difference equations on non-uniform lattices: dynamical algebra.
COSTAS SANTOS, ROBERTO SANTIAGO
01/07/2005
Ponencia del Congreso
Number Theory, q-calculus. The zeta and q-zeta functions.
COSTAS SANTOS, ROBERTO SANTIAGO
01/07/2004
Ponencia del Congreso

Book chapters and books

Book chapters and books
Applications and q-Extensions of Hypergeometric Functions
01/01/2025
Libro Completo
Classical hypergeometric functions and generalizations
01/01/2025
Libro Completo
Double summation addition theorems for Jacobi functions of the first and second kind
01/01/2025
Capítulo de un Libro
Sobolev orthogonal polynomials: Connection formulae
23/12/2022
Capítulo de un Libro
Actas del XIII Congreso de Tecnología, Aprendizaje y Enseñanza de la Electrónica
22/06/2018
Capítulo de un Libro
The orthogonality of Al-Salam-Carlitz polynomials for complex parameters
01/01/2018
Capítulo de un Libro
ATICA 2016. Aplicaciones de Tecnologías de la Información y Comunicaciones Avanzadas.
09/11/2016
Capítulo de un Libro

External research projects

External Projects
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