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List of Publications

In preparation

  1. Proof of an Extension of The Hankel Pencil Conjecture using Orthogonal Polynomials (With C R Johnson)
  2. Irrationality proofs of Zeta(3), Zeta(5) and Zeta(7).
  3. Countour integral representations for elliptic hypergeometric functions (with H S Cohl)
  4. On the linearization coefficients for continuous q-Jacobi and continuous q-ultraspherical polynomials (with H S Cohl)
  5. The top of semiclassical orthogonal polynomials: The $N$-Askey-Wilson polynomials
  6. Semiclassical quasi-orthogonal polynomials. A general difference calculus approach (with F Marcellan)
  7. The orthogonality of the $q$-Laguerre for a general parameter (with F Marcellan)
  8. Generating functions of Classical polynomials satisfying Laguerre-type Second structure relation (with J F Mañas-Mañas, J J Moreno-Balcazar)
  9. Algebraic and orthogonality properties of someq-analogs of the Laguerre polynomials for non classical parameters (with M T Perez, M Piñar)
  10. 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 ..., 2022 | [Arx]
  3. Classical exceptional orthogonal polynomials: a global overview (With J S Kelly) | Submitted to Asian Journal of Mathematics, 2022 | [Arx]
  4. The permanent of a sum of matrices | 2022
  5. Localization of zeros of polar polynomials (with A Rehouma) | 2022

Papers

  1. Symmetry of terminating series representations of the Askey-Wilson polynomials
    Cohl, H. S. and Costas-Santos, R. S. Journal of Mathematical Analysis and Applications. Accepted in 2022
  2. On polynomials orthogonal with respect to an inner product involving higher order differences. The Meixner case
    Costas-Santos, R. S., Soria-Lorente, A. and Vilaire J.-M. Mathematics 10 no. 11 (2022), 1952
  3. Generalizations of generating functions for basic hypergeometric orthogonal polynomials
    Cohl, H. S., Costas-Santos, R. S., Hwang, P. R. and Wakhare, T. V . Open Journal of Mathematical Sciences. Accepted in 2022
  4. On the relation between Gegenbauer polynomials and the Ferrers function of the first kind
    Cohl, H. S., Costas-Santos, R. S. Analysis Mathematica. Accepted in 2021
  5. Utility of integral representations for basic hypergeometric functions and orthogonal polynomials
    Cohl, H. S., Costas-Santos, R. S. The Ramanujan Journal. Special Volume Dedicated to Dick Askey. Accepted in 2021
  6. Multi-integral representations for associated Legendre and Ferrers functions
    Cohl, H. S., Costas-Santos, R. S. Symmetry 12, no. 10, 1598 (2020), 22 pages
  7. Terminating basic hypergeometric representations and transformations for the Askey-Wilson polynomials
    Cohl, H. S., Costas-Santos, R. S., and Ge, L. Symmetry 2 no. 8 (2020), 1290
  8. On a generalization of the Rogers generating function
    Cohl, H. S., Costas-Santos, R. S., and Wakhare, T. V. Journal of Mathematical Analysis and Applications 475, no. 2 (2019), 1019 — 1043
  9. Some generating functions for q-polynomials
    Cohl, H. S., Costas-Santos, R. S., and Wakhare, T. V. Symmetry-Basel 10, no. 12 (2018), 300 — 311
  10. Analytic properties of some basic hypergeometric-Sobolev-type orthogonal polynomials
    Costas-Santos, Roberto S. and Soria-Lorente, A. Journal of Difference Equations and Applications 24, no. 11 (2018), 1715 — 1733
  11. The power collection method for connection relations: Meixner polynomials
    Baeder, M. A.; Cohl, H. S., Costas-Santos, R. S. and Xu, W. Journal of Classical Analysis Volume 11, no. 2 (2017), 107 — 128
  12. The orthogonality of Al-Salam-Carlitz polynomials for complex parameters
    Cohl, H. S., Costas-Santos, R. S. and Xu, W. 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.
  13. Matrices Totally Positive Relative to a Tree, II
    Costas-Santos, R. S. and Johnson, C. R. Linear Algebra and its Applications 505 (2016), 1 — 10
  14. Zeros of polynomials orthogonal with respect to a signed weight
    Atia, M. J.; Benabdallah, M. and Costas-Santos, R. S. Indagationes Mathematicae 23 no. 1-2 (2012), 26 — 31
  15. 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
  16. 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
  17. 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
  18. q-Classical orthogonal polynomial: A general difference calculus approach
    Costas-Santos, R. S.and Marcellan, F. Acta Applicandae Mathematicae 111 (2010), 107 — 128
  19. 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
  20. 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
  21. Matrices Totally Positive Relative to a Tree
    Johnson, C. R.; Costas-Santos, R. S. and Tadchiev, B. Electronic Journal of Linear Algebra 18 (2009), 211 — 221
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. Principal minor sums of (A+tB)m
    Johnson, C. R.; Leichenauer, S.; MacNamara, P. R. W. and Costas, R. Linear Algebra and its Applications 411 (2005), 386 — 389
  28. 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