In preparation
  1. Irrationality proofs of Zeta(3), Zeta(5) and Zeta(7).
  2. The top of semiclassical orthogonal polynomials: The $N$-Askey-Wilson polynomials
  3. {provisional} A generalization of Euler-Frobenious polynomials through classical linear functional
  4. Semiclassical quasi-orthogonal polynomials. A general difference calculus approach (with F Marcellan)
  5. The orthogonality of the $q$-Laguerre for a general parameter (with F Marcellan)
  6. {provisional}The orthogonality of the big $q$-Jacobi for general parameters (with A Soria-Lorente)
  7. {provisional} Zeros of krall-type orthogonal polynomials. A one mass-point general study (with A Soria-Lorente)
  8. Analytic properties of some basic hypergeometric-Sobolev type orthogonal polynomials (with A Soria-Lorente)
Preprints
  1. Some generating functions of $q$-polynomials (with H. Cohl) | [Overleaf] Preprint
  2. Al-Salam-Carlitz polynomials. A general study (with H. Cohl, W. Xu) | [Overleaf] Preprint
  3. Maximal Meixner generalized generating functions for Meixner polynomials (with M. A. Baeder, H. Cohl, W. Xu) | [Overleaf] Preprint
  4. On polynomials defined by a modified Rodrigues formula (with F. Marcellan) | Submitted to AMC
  5. Generalizations of generating functions for basic hypergeometric orthogonal polynomials (with H. Cohl, P. Hwang)
    [Overleaf] Submitted to BMAA
  6. Matrices Totally Positive Relative to a Tree, II | [Arx] Submitted to LAA
Papers [MR:13] [Zbl:14] [Arx:13] [BiBTeX:15]
  1. 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},
    }				 
  2. 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
                  Marcell{\'a}n},
         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},
    }				 
  3. 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 S{\'a}nchez-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},
    }				 
  4. 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-Balc\'azar, 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}
    }
    				 
  5. 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.; Marcellán, 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}
    }
    				 
  6. 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.; Sánchez-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}
    }
    				 
  7. 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)}
    }
    				 
  8. 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 Marijuán}
    }
    				 
  9. 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.; Marcellán, 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}
    }
    				 
  10. 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 = {Alvarez-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}
    }
    				 
  11. 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}
    }
    				 
  12. 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}
    }
    				 
  13. 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}
    }
    				 
  14. 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}
    }
    				 
  15. 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}
    }
    				 
Unpublished works
  1. Integral representations for a generalized Hermite linear functional (with R. Sfaxi) | [Arx]