In preparation
- Irrationality proofs of Zeta(3), Zeta(5) and Zeta(7).
- The top of semiclassical orthogonal polynomials: The $N$-Askey-Wilson polynomials
- {provisional} A generalization of Euler-Frobenious polynomials through classical linear functional
- Semiclassical quasi-orthogonal polynomials. A general difference calculus approach (with F Marcellan)
- Classical Orthogonal Polynomials and generalized Stieltjes transforms
- Generalizations of generating functions for basic hypergeometric orthogonal polynomials (with H Cohl, P Hwang, T V Wakhare)
- {provisional} Zeros of krall-type orthogonal polynomials. A one mass-point general study (with A Soria-Lorente)
- The orthogonality of the $q$-Laguerre for a general parameter (with F Marcellan)
- {provisional}A Deep study of the big q-Jacobi polynomials in the complex plane (with A Soria-Lorente, E J Huertas)
- Exceptional orthogonal polynomials from the semi-classical point of view (With J S Kelly)
- Zeros of q-Krall Orthogonal Polynomials (With O Bihun)
- Generating functions of Classical polynomials satisfying Laguerre-type Second structure relation (with J F Mañas-Mañas, J J Moreno-Balcazar)
- Algebraic and orthogonality properties of some q-analogs of the Laguerre polynomials for non classical parameters (with M T Perez, M Piñar)
- On polynomials defined by a modified Rodrigues formula (with F Marcellan)
Preprints
- Integral representations for a generalized Hermite linear functional (with R. Sfaxi) | Submitted to Axioms, 2019 | [Arx]
- Spectra of Tridiagonal Matrices over a Field (with C R Johnson) | Submitted to LaMA, 2019 | [Arx]
- Generalizations of linearization formulae for continuous hypergeometric orthogonal polynomials (with H S Cohl and J Zhao) | 2018
- Associated functions from Rodrigues' Formula for Classical Orthogonal polynomials | 2019
- On a generalization of the Rogers generating function (with H Cohl and T V Wakhare) | J. Math. Anal. Appl. 475 (2019),
no. 2, 1019--1043 | DOI: 10.1016/j.jmaa.2019.01.068 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR3944361, AUTHOR = {Cohl, Howard S. and Costas-Santos, Roberto S. and Wakhare, Tanay V.}, TITLE = {On a generalization of the {R}ogers generating function}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {475}, YEAR = {2019}, NUMBER = {2}, PAGES = {1019--1043}, ISSN = {0022-247X}, MRCLASS = {33D05}, MRNUMBER = {3944361}, DOI = {10.1016/j.jmaa.2019.01.068}, URL = {https://doi.org/10.1016/j.jmaa.2019.01.068}, }
- Some generating functions for $q$-polynomials (with H Cohl and T V Wakhare) Symmetry, 10, 12, 758, 12 pages (2018)
DOI: 10.3390/sym10120758 | [MR] [Zbl] [Arx] [GS?] [BibTeX] - Analytic properties of some basic hypergeometric-Sobolev-type orthogonal polynomials (with A Soria-Lorente)
J. Difference Equ. Appl. 24 (2018), no. 11, 1715--1733 | DOI: 10.1080/10236198.2018.1517760 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR3883341, AUTHOR = {Costas-Santos, Roberto S. and Soria-Lorente, Anier}, TITLE = {Analytic properties of some basic hypergeometric-{S}obolev-type orthogonal polynomials}, JOURNAL = {J. Difference Equ. Appl.}, FJOURNAL = {Journal of Difference Equations and Applications}, VOLUME = {24}, YEAR = {2018}, NUMBER = {11}, PAGES = {1715--1733}, ISSN = {1023-6198}, MRCLASS = {33D45 (05A30 39A13)}, MRNUMBER = {3883341}, DOI = {10.1080/10236198.2018.1517760}, URL = {https://doi.org/10.1080/10236198.2018.1517760}, }
- The power collection method for connection relations: Meixner polynomials (with M A Baeder, H S Cohl and W Xu)
Journal of Classical Analysis. Volume 11, Number 2 (2017), 107--128 | DOI: 10.7153/jca-11-02 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR3745468, AUTHOR = {Baeder, Michael A. and Cohl, Howard S. and Costas-Santos, Roberto S. and Xu, Wenqing}, TITLE = {The power collection method for connection relations: {M}eixner polynomials}, JOURNAL = {J. Class. Anal.}, FJOURNAL = {Journal of Classical Analysis}, VOLUME = {11}, YEAR = {2017}, NUMBER = {2}, PAGES = {107--128}, ISSN = {1848-5979}, MRCLASS = {33C45 (05A15 30C10 30E20 33C20)}, MRNUMBER = {3745468}, DOI = {10.7153/jca-2017-11-08}, URL = {https://doi.org/10.7153/jca-2017-11-08}, }
- The orthogonality of Al-Salam-Carlitz polynomials for complex parameters (with H Cohl and W Xu)
Frontiers in Orthogonal Polynomials and q-Series, Contemporary Mathematics and its Applications: Monographs, Expositions
and Lecture Notes, Eds. Zuhair Nashed and Xin Li, Vol. 1, Chapter 8, 155--167, World Scientific Publishing Company,
Cambridge, MA, 2018. | ISSN-13: 9789813228870 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@incollection {MR3791613, AUTHOR = {Cohl, Howard S. and Costas-Santos, Roberto S. and Xu, Wenqing}, TITLE = {The orthogonality of {A}l-{S}alam--{C}arlitz polynomials for complex parameters}, BOOKTITLE = {Frontiers in orthogonal polynomials and {$q$}-series}, SERIES = {Contemp. Math. Appl. Monogr. Expo. Lect. Notes}, VOLUME = {1}, PAGES = {155--167}, PUBLISHER = {World Sci. Publ., Hackensack, NJ}, YEAR = {2018}, MRCLASS = {33C47 (42C05)}, MRNUMBER = {3791613}, }
- Matrices Totally Positive Relative to a Tree, II (with C
R Johnson) Linear Algebra Appl. 505 (2016), 1--10
DOI:10.1016/j.laa.2016.04.021 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR3506481, AUTHOR = {Costas-Santos, R. S. and Johnson, C. R.}, TITLE = {Matrices totally positive relative to a tree, {II}}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {505}, YEAR = {2016}, PAGES = {1--10}, ISSN = {0024-3795}, MRCLASS = {15B48 (05C05 05C50 15A18 94C15)}, MRNUMBER = {3506481}, MRREVIEWER = {Carlos Marijuan}, DOI = {10.1016/j.laa.2016.04.021}, URL = {http://dx.doi.org/10.1016/j.laa.2016.04.021}, }
- Zeros of polynomials orthogonal with respect to a signed weight (with M Benabdallah and M J Atia) Indag. Math. (N.S.) 23 (2012),
no. 1-2, 26-31 | DOI:10.1016/j.cam.2008.07.055 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR2877399, AUTHOR = {Atia, M. J. and Benabdallah, M. and Costas-Santos, R. S.}, TITLE = {Zeros of polynomials orthogonal with respect to a signed weight}, JOURNAL = {Indag. Math. (N.S.)}, FJOURNAL = {Koninklijke Nederlandse Akademie van Wetenschappen. Indagationes Mathematicae. New Series}, VOLUME = {23}, YEAR = {2012}, NUMBER = {1-2}, PAGES = {26--31}, ISSN = {0019-3577}, MRCLASS = {33C45 (42C05)}, MRNUMBER = {2877399 (2012m:33007)}, MRREVIEWER = {Serhan Varma}, DOI = {10.1016/j.indag.2011.09.011}, URL = {http://dx.doi.org/10.1016/j.indag.2011.09.011}, }
- The complementary polynomials and the Rodrigues operator of COP (with F Marcellan) Proc. AMS 140(10) (2012), 3485--3493
DOI:10.1090/S0002-9939-2012-11229-8 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR2929017, AUTHOR = {Costas-Santos, Roberto S. and Espa{\~n}ol, Francisco Marcellan}, TITLE = {The complementary polynomials and the {R}odrigues operator of classical orthogonal polynomials}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {140}, YEAR = {2012}, NUMBER = {10}, PAGES = {3485--3493}, ISSN = {0002-9939}, CODEN = {PAMYAR}, MRCLASS = {33C45 (33D45 34B24 39A13 42C05)}, MRNUMBER = {2929017}, MRREVIEWER = {Roelof Koekoek}, DOI = {10.1090/S0002-9939-2012-11229-8}, URL = {http://dx.doi.org/10.1090/S0002-9939-2012-11229-8}, }
- Orthogonality of q-polynomials for nonstandard parameters (with J F Sanchez-Lara) J. Approx. Theory 163 (2011), no. 9,
1246--1268 | DOI:10.1016/j.jat.2011.04.005 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR2832754, AUTHOR = {Costas-Santos, R. S. and Sanchez-Lara, J. F.}, TITLE = {Orthogonality of {$q$}-polynomials for non-standard parameters}, JOURNAL = {J. Approx. Theory}, FJOURNAL = {Journal of Approximation Theory}, VOLUME = {163}, YEAR = {2011}, NUMBER = {9}, PAGES = {1246--1268}, ISSN = {0021-9045}, CODEN = {JAXTAZ}, MRCLASS = {33D45}, MRNUMBER = {2832754 (2012f:33027)}, MRREVIEWER = {Ulrich Tamm}, DOI = {10.1016/j.jat.2011.04.005}, URL = {http://dx.doi.org/10.1016/j.jat.2011.04.005}, }
- The Semiclassical-Sobolev orthogonal polynomials: A general approach (with J J Moreno-Balcazar) J. Approx. Theory, 163 (2011),
no. 1, 65--83 | DOI:10.1016/j.jat.2010.03.001 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR2741220, AUTHOR = {Costas-Santos, R.S. and Moreno-Balcázar, J.J.}, TITLE = {The semiclassical Sobolev orthogonal polynomials: a general approach}, JOURNAL = {J. Approx. Theory}, FJOURNAL = {Journal of Approximation theory}, VOLUME={163}, NUMBER={1}, PAGES={65--83}, YEAR = {2011}, ISSN = {0167-8019}, DOI={10.1016/j.jat.2010.03.001}, MRCLASS = {33C45 (42C05)}, MRNUMBER = {MR2741220} }
- q-Classical orthogonal polynomial: A general difference calculus approach (with F Marcellan) Acta Appl. Math. 2009.
DOI:10.1007/s10440-009-9536-z | [MR][Zbl] [Arx] [GS?] [BibTeX]@article {MR2653053, AUTHOR = {Costas-Santos, R. S.; Marcellan, F.}, TITLE = {$q$-Classical Orthogonal Polynomials: A General Difference Calculus Approach}, JOURNAL = {Acta Appl. Math.}, FJOURNAL = {Acta Applicandae Mathematicae}, YEAR = {2009}, ISSN = {0167-8019}, MRCLASS = {33C45 (33D45)}, MRREVIEWER = {Thomas Stoll} }
- Extensions of discrete classical orthogonal polynomials beyond the orthogonality (with J F Sanchez-Lara)
J. Comput. Appl. Math. 225 (2009), no. 2, 440--451. | DOI:10.1016/j.cam.2008.07.055 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR2494714, AUTHOR = {Costas-Santos, R. S.; Sanchez-Lara, J. F.}, TITLE = {Extensions of discrete classical orthogonal polynomials beyond the orthogonality}, JOURNAL = {J. Comput. Appl. Math.}, FJOURNAL = {Journal of Computational and Applied Mathematics}, VOLUME = {225}, NUMBER={2}, YEAR = {2009}, PAGES = {440--451}, ISSN = {1081-3810}, MRCLASS = {33C45 (33C47 42C05)}, MRNUMBER = {MR2494714}, MRREVIEWER = {Alicia Cachafeiro} }
- On the elementary symmetric functions of a sum of matrices J. Algebra Number Theory, Adv. Appl. 1 (2009), No. 2, 99-112.
[MR] [Zbl] [Arx] [GS?] [BibTeX]@article {cos1, AUTHOR = {Costas-Santos, Roberto S.}, TITLE = {On the elementary symmetric functions of a sum of matrices}, JOURNAL = {J. Algebra Number Theory, Adv. Appl.}, FJOURNAL = {Journal of Algebra, Number Theory: Advances and Applications}, VOLUME = {1}, NUMBER={2}, YEAR = {2009}, PAGES = {99--112}, ISSN = {0975-1548}, MRCLASS = {11C20 (05E05 11P81)} }
- Matrices Totally Positive Relative to a Tree (with C R Johnson and B Tadchiev) Electron. J. Linear Algebra 18 (2009), 211--221.
[MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR2505131, AUTHOR = {Johnson, Charles R.; Costas-Santos, Roberto S.; Tadchiev, Boris}, TITLE = {Matrices totally positive relative to a tree}, JOURNAL = {Electron. J. Linear Algebra}, FJOURNAL = {Electronic Journal of Linear Algebra}, VOLUME = {18}, YEAR = {2009}, PAGES = {211--221}, ISSN = {1081-3810}, MRCLASS = {15B48 (05C05 05C50 15A18 94C15)}, MRNUMBER = {MR2505131}, MRREVIEWER = {Carlos Marijuan} }
- Second structure relation for q-semiclassical polynomials of the Hahn Tableau (with F Marcellan) J. Math. Anal. Appl. 329 (2007),
no. 1, 206--228 | DOI:10.1016/j.jmaa.2006.06.036 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR2306798, AUTHOR = {Costas-Santos, R. S.; Marcellan, F.}, TITLE = {Second structure relation for $q$-semiclassical polynomials of the Hahn Tableau}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {329}, NUMBER={1}, YEAR = {2007}, PAGES = {206--228}, ISSN = {0022-247X}, MRCLASS = {33D45}, MRNUMBER = {MR2306798}, MRREVIEWER = {Qing-Hu Hou} }
- Factorization of the hypergeometric-type difference equation on the uniform lattice (with R Alvarez-Nodarse and N M Atakishiyev)
Electron. Trans. Numer. Anal. 27 (2007), 34--50 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR2346147, AUTHOR = {Álvarez-Nodarse, R.; Atakishiyev, N. M.; Costas-Santos, R. S.}, TITLE = {Factorization of the hypergeometric-type difference equation on the uniform lattice}, JOURNAL = {Electron. Trans. Numer. Anal.}, FJOURNAL = {Electronic Transactions on Numerical Analysis}, VOLUME = {27}, YEAR = {2007}, PAGES = {34--50}, ISSN = {1068-9613}, MRCLASS = {33C45 (33C90 39A13)}, MRNUMBER = {MR2346147}, MRREVIEWER = {Stefan Gerhold} }
- A q-analog of the Racah polynomials and q-algebra SUq(2) in quantum optics (with R Alvarez-Nodarse and Y F Smirnov) J. Russ.
Laser. Res. Volume 27, Number 1 (January 2006), 1--32. | DOI:10.1007/s10946-006-0001-4 | [MR] [Zbl] [Arx] [ GS?] [BibTeX]@article {alvcos1, AUTHOR = {Álvarez-Nodarse, R.; Costas-Santos, R. S.}, TITLE = {Limit relations between $q$-Krall type orthogonal polynomials}, JOURNAL = {J. Russ. Laser. Res.}, FJOURNAL = {Journal of Russian Laser Research}, VOLUME = {27}, NUMBER={1}, YEAR = {2006}, PAGES = {1--32}, ISSN = {1071-2836} }
- Limit relations between q-Krall type orthogonal polynomials (with R Alvarez-Nodarse) J. Math. Anal. Appl. 322 (2006), no. 1,
158--176 | DOI:10.1016/j.jmaa.2005.08.067 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR2238156, AUTHOR = {Álvarez-Nodarse, R.; Costas-Santos, R. S.}, TITLE = {Limit relations between $q$-Krall type orthogonal polynomials}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {322}, NUMBER={1}, YEAR = {2006}, PAGES = {158--176}, ISSN = {0022-247X}, MRCLASS = {33C45 (42C05)}, MRNUMBER = {MR2238156}, MRREVIEWER = {Youssèf Ben Cheikh} }
- Factorization of the hypergeometric-type difference equation on non-uniform lattices: dynamical algebra (with R Alvarez-Nodarse
and N M Atakishiyev) J. Phys. A 38 (2005), no. 1, 153--174 | DOi:10.1088/0305-4470/38/1/011 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR2126099, AUTHOR = {Álvarez-Nodarse, R.; Atakishiyev, N. M.; Costas-Santos, R. S.}, TITLE = {Factorization of the hypergeometric-type difference equation on non-uniform lattices: dynamical algebra}, JOURNAL = {J. Phys. A}, FJOURNAL = {Journal of Physics. A. Mathematical and Theoretical}, VOLUME = {38}, NUMBER={1}, YEAR = {2005}, PAGES = {153--174}, ISSN = {1751-8113}, MRCLASS = {39A13 (33D15)}, MRNUMBER = {MR2126099}, MRREVIEWER = {Lucia Di Vizio} }
- Principal minor sums of (A+tB)^m (with Charles R Johnson, Stefan Leichenauer, and Peter McNamara) Linear Algebra Appl. 411
(2005), 386--389. | DOI:10.1016/j.laa.2005.06.018 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR2178699, AUTHOR = {Johnson, Charles R.; Leichenauer, Stefan; McNamara, Peter; Costas, Roberto}, TITLE = {Principal minor sums of $(A+tB)^m$}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {411}, YEAR = {2005}, PAGES = {386--389}, ISSN = {0024-3795}, MRCLASS = {15A15 (15A57)}, MRNUMBER = {MR2178699}, MRREVIEWER = {Peter M. Gibson} }
- Factorization method for difference equations of hypergeometric type on nonuniform lattices (with R Alvarez-Nodarse)
J. Phys. A: Math. Gen. 34 (2001), no. 27, 5551?5569. | DOI:10.1088/0305-4470/34/27/306 | [MR] [Zbl] [Arx] [GS?] [BibTeX]@article {MR1856663, AUTHOR = {Álvarez-Nodarse, R.; Costas-Santos, R. S.}, TITLE = {Factorization method for difference equations of hypergeometric type on nonuniform lattices}, JOURNAL = {J. Phys. A}, FJOURNAL = {Journal of Physics. A. Mathematical and Theoretical}, VOLUME = {34}, NUMBER={27}, YEAR = {2001}, PAGES = {5551--5569}, ISSN = {1751-8113}, MRCLASS = {39A13 (33C45 33D45)}, MRNUMBER = {MR1856663}, MRREVIEWER = {A. M. Gavrilik} }