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List of Publications


    In preparation

    1. The subpermanent of a sum of matrices (With C R Johnson)
    2. Proof of an Extension of The Hankel Pencil Conjecture using Orthogonal Polynomials (With C R Johnson)
    3. Irrationality proofs of Zeta(3), Zeta(5) and Zeta(7).
    4. Countour integral representations for elliptic hypergeometric functions (with H S Cohl)
    5. On the linearization coefficients for continuous q-Jacobi and continuous q-ultraspherical polynomials (with H S Cohl)
    6. The top of semiclassical orthogonal polynomials: The $N$-Askey-Wilson polynomials
    7. Semiclassical quasi-orthogonal polynomials. A general difference calculus approach (with F Marcellan)
    8. The orthogonality of the $q$-Laguerre for a general parameter (with F Marcellan)
    9. Generating functions of Classical polynomials satisfying Laguerre-type Second structure relation (with J F Mañas-Mañas, J J Moreno-Balcazar)
    10. Algebraic and orthogonality properties of someq-analogs of the Laguerre polynomials for non classical parameters (with M T Perez, M Piñar)
    11. On polynomials defined by a modified Rodrigues formula (with F Marcellan)

    Preprints

    1. Integral representations for a generalized Hermite linear functional (with R. Sfaxi) | Submitted to Axioms, 2019 | [Arx]
    2. Spectra of Tridiagonal Matrices over a Field (with C R Johnson) | Submitted to Bulletin of the Iranian Mathematical Society, 2021 | [Arx]
    3. Generalizations of generating functions for basic hypergeometric orthogonal polynomials (with H S Cohl, P R Hwang
      and T V Wakhare) | Submitted to , 2021
    4. On polynomials orthogonal with respect to an inner product involving higher order differences. The Meixner case
      (With A Soria, J.-M. Vilaire) | Submitted to The Ramanujan Journal, 2020 | [Arx]
    5. Classical exceptional orthogonal polynomials: a global overview (With J S Kelly) | Submitted to ..., 2021 | Arx]

    Papers

    1. On the relation between Gegenbauer polynomials and the Ferrers function of the first kind
      Howard S Cohl, R S Costas-Santos. Analysis Mathematica Accepted in 2021
    2. Utility of integral representations for basic hypergeometric functions and orthogonal polynomials
      Howard S Cohl, R S Costas-Santos. Accepted in Ramanujan Journal (2021) | SPRINGER (NETHERLANDS) | ISSN: 1382-4090
      JCR® 2020 Impact Factor: 0.837 - MATHEMATICS -- position: 202/330 (Q3/T2) | MR Zbl] [Arx] [GS?] BibTeX]
    3. Multi-integral representations for associated Legendre and Ferrers functions (with H Cohl)
      Symmetry 12 No. 10, 1598 (2020), 22 pages | MDPI (SWITZERLAND) | DOI: 10.3390/sym12101598
      JCR® 2020 Impact Factor: 2.713 - MULTIDISCIPLINARY SCIENCES -- position: 33/73 (Q2/T2) | | MR] [Zbl] [Arx] [GS?] [BibTeX]
      @Article{cohcos,
       Author = {Howard S. Cohl and Roberto S. Costas-Santos},
       Title = {Multi-integral representations for associated Legendre and Ferrers functions},
       FJournal = {Symmetry},
       Journal = {Symmetry},
       ISSN = {2073-8994},
       Volume = {12},
       Number = {10},
       Pages = {22},
       Note = {Id/No 1598},
       Year = {2020},
       Publisher = {Multidisciplinary Digital Publishing Institute (MDPI), Basel},
       Language = {English},
       DOI = {10.3390/sym12101598},
       MSC2010 = {33C45}
      }
      
    4. Terminating basic hypergeometric representations and transformations for the Askey-Wilson polynomials (with H Cohl and L Ge)
      Symmetry 12(8) (2020), 1290 | DOI: 10.3390/sym12081290
      JCR® 2020 Impact Factor: 2.713 - MULTIDISCIPLINARY SCIENCES -- position: 33/73 (Q2/T2) | MR] [Zbl] [Arx] [GS?] [BibTeX]
      @Article{Cohletall2020,
       Author = {Cohl, Howard S. and Costas-Santos, Roberto S. and Ge, Linus},
       Title = {Terminating basic hypergeometric representations and transformations for the Askey-Wilson polynomials},
       FJournal = {Symmetry},
       Journal = {Symmetry},
       ISSN = {2073-8994},
       Volume = {12},
       Number = {8},
       Pages = {14},
       Note = {Id/No 1290},
       Year = {2020},
       Publisher = {Multidisciplinary Digital Publishing Institute (MDPI), Basel},
       Language = {English},
       DOI = {10.3390/sym12081290},
       MSC2010 = {33D45},
       Zbl = {1456.33013}
      }
      
    5. 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 | ACADEMIC PRESS INC ELSEVIER SCIENCE (USA) | ISSN: 0022-247X | DOI: 10.1016/j.jmaa.2019.01.068
      JCR® 2019 Impact Factor: 1.220 - MATHEMATICS -- position: 77/325 (Q1/T1) | [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},
      }
      
    6. Some generating functions for $q$-polynomials (with H Cohl and T V Wakhare)
      Symmetry-Basel 10(12), 758, 300--311 (2018) | MDPI (SWITZERLAND) | ISSN: 2073-8994 | DOI: 10.3390/sym10120758
      JCR® 2018 Impact Factor: 2.143 - MULTIDISCIPLINARY SCIENCES -- position: 30/69 (Q2/T2) | MR] [Zbl] [Arx] [GS?] [BibTeX]
      @article {Cohletall2018,
       AUTHOR = {Cohl, Howard S., Costas-Santos, Roberto S. and Wakhare, Tanay},
       TITLE = {Some generating functions for $q$-polynomials},
       JOURNAL = {Symmetry},
       FJOURNAL = {Symmetry},
       VOLUME = {10},
       YEAR = {2018},
       NUMBER = {12},
       PAGES = {758, 12 pages},
       ISSN = {2073-8994},
       DOI = {10.3390/sym10120758},
       URL = {https://doi.org/10.3390/sym10120758},
      }				
    7. Analytic properties of some basic hypergeometric-Sobolev-type orthogonal polynomials (with A Soria-Lorente)
      J. Difference Equ. Appl. 24, no. 11 (2018), 1715--1733 | TAYLOR \& FRANCIS LTD (UK) | ISSN: 1023-6198 | DOI: 10.1080/10236198.2018.1517760
      JCR® 2018 Impact Factor: 0.974 - APPLIED MATHEMATICS -- position: 149/254 (Q3/T2) | [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},
      }				
    8. 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 | JCA (CROATIA) I ISSN: 1848-5987
      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},
      }				
    9. 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},
      }
      
    10. Matrices Totally Positive Relative to a Tree, II
      Costas-Santos, R. S. and Johnson, Charles R. Linear Algebra and its Applications 505 (2016), 1 — 10
    11. Zeros of polynomials orthogonal with respect to a signed weight
      Atia, M. J.; Benabdallah M. and Costas-Santos, R.S. Indagationes Mathematicae. New Series 23 no. 1-2 (2012), 26 — 31
    12. The complementary polynomials and the Rodrigues operator of classical orthogonal polynomials
      Costas-Santos, R. S. and Marcellan, F. Proceedings of the American Mathematical Society 140, no. 10 (2012), 3485 — 3493
    13. Orthogonality of q-polynomials for non-standard parameters
      Costas-Santos, R. S. and Sanchez-Lara, J. F. Journal of Approximation Theory 163, no. 9 (2011), 1246 —1268
    14. The Semiclassical-Sobolev orthogonal polynomials: A general approach
      Costas-Santos, R. S. and Moreno Balcazar, J. J. Journal of Approximation theory 163, no. 1 (2011), 65 — 83
    15. q-Classical orthogonal polynomial: A general difference calculus approach
      Costas-Santos, R. S.and Marcellan, F. Acta Applicandae Mathematicae 111 (2010), 107 — 128
    16. Extensions of discrete classical orthogonal polynomials beyond the orthogonality
      Costas-Santos, R. S. and Sanchez-Lara, J. F. Journal of Computational and Applied Mathematics 225, no. 2 (2009), 440 — 451
    17. On the elementary symmetric functions of a sum of matrices
      Costas-Santos, R. S. JP Journal of Algebra, Number Theory: Advances and Applications 1, No. 2 (2009), 99 — 112
    18. Matrices Totally Positive Relative to a Tree
      Johnson, Charles R.; Costas-Santos, Roberto S. and Tadchiev, Boris Electronic Journal of Linear Algebra 18 (2009), 211 — 221
    19. Second structure relation for q-semiclassical polynomials of the Hahn Tableau
      Marcellan, F. and Costas-Santos, R. S. Journal of Mathematical Analysis and Applications 329, no. 1 (2007), 206 — 228
    20. Factorization of the hypergeometric-type difference equation on the uniform lattice
      Álvarez-Nodarse, R.; Atakishiyev, N. M. and Costas-Santos, R. S. Electronic Transactions on Numerical Analysis 27 (2007), 34 — 50
    21. A q-analog of the Racah polynomials and q-algebra SUq(2) in quantum optics
      Álvarez-Nodarse, R.; Costas-Santos, R. S. and Smirnov, Y. F. Journal of Russian Laser Research Volume 27, Number 1 (January 2006), 1 — 32
    22. Limit relations between q-Krall type orthogonal polynomials
      Álvarez-Nodarse, R. and Costas-Santos, R. S. Journal of Mathematical Analysis and Applications 322, no. 1 (2006), 158 — 176
    23. Factorization of the hypergeometric-type difference equation on non-uniform lattices: dynamical algebra
      Álvarez-Nodarse, R.; Atakishiyev, N. M. and Costas-Santos, R. S. Journal of Physics A. Mathematical and General 38, no. 1 (2005), 153 — 174
    24. Principal minor sums of (A+tB)m
      Johnson, C. R.; Leichenauer, S.; MacNamara, P. and Costas, R. Linear Algebra and its Applications 411 (2005), 386 — 389
    25. Factorization method for difference equations of hypergeometric type on nonuniform lattices
      Álvarez-Nodarse, R. and Costas-Santos, R. S. Journal of Physics A: Mathematical and General volume 34, no. 27 (2001), 5551 — 5569