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Papers and Preprints

In preparation

  1. Irrationality proofs of \(\zeta(3)\), \(\zeta(5)\) and \(\zeta(7)\).
  2. Semiclassical quasi-orthogonal polynomials. A general difference calculus approach (with F Marcellan)
  3. On the linearization coefficients for continuous \(q\)-Jacobi and continuous \(q\)-ultraspherical polynomials (with H S Cohl)
  4. The top of semiclassical orthogonal polynomials: The \(N\)-Askey-Wilson polynomials
  5. The orthogonality of the \(q\)-Laguerre for a general parameter (with F Marcellan)
  6. Algebraic and orthogonality properties of some \(q\)-analogs of the Laguerre polynomials for non classical parameters (with M T Perez, M Piñar)
  7. On polynomials defined by a modified Rodrigues formula (with F Marcellan)
  8. Proof of an Extension of The Hankel Pencil Conjecture using Orthogonal Polynomials (With C R Johnson)
  9. Zeros of Al-Salam-Carlitz polynomials. The real parameters case
  10. Zeros of Krawtchouk Sobolev-type Orthogonal polynomials. A numerical study (With A Soria Lorente)
  11. Generating functions of Classical polynomials satisfying Laguerre-type Second structure relation (with J F Mañas-Mañas, J J Moreno-Balcazar)
  12. Generating functions for the \(q\) and \(q^{-1}\)-symmetric polynomials in the \(q\)-Askey scheme (With H S Cohl)
  13. Recurrence relations associated to rational approximations of \(\zeta(7)\). A first study (With A Soria Lorente)

Preprints

  1. Polynomial solutions of recurrence derivatives with negative indices | [Arx] | 2025
  2. On polar Meixner polynomials | [Arx] | 2025
  3. The degenerate Krall–Laguerre polynomials | [Arx] | 2025
  4. The \(\xi\)−Laguerre polynomials | [Arx] | 2025
  5. The permanent of a sum of matrices | [Arx] | 2025
  6. Spectra of Tridiagonal Matrices over a Field (with C R Johnson) | [Arx] | 2025
  7. Classical exceptional orthogonal polynomials: a global overview (With J S Kelly) | [Arx] | 2025
  8. Asymptotics, orthogonality relations and duality for the \(q\) and \(q^{-1}\)-symmetric polynomials in the \(q\)-Askey scheme (With H S Cohl
    and X.-S. Wang) | [Arx]| 2025
  9. The \(q\) and \(q^{-1}\)-symmetric and dual orthogonal polynomials in the \(q\)-Askey scheme: generating functions, orthogonality and \(q\)-Chaundy representation
    (With H S Cohl) | [Arx] | Submitted, 2025

Papers

  1. Special values for continuous \(q\)-Jacobi polynomials with application to its Poisson kernel ||
    Cohl, H. S. and Costas-Santos, R. S. Proceedings of the 16th International Symposium on Orthogonal Polynomials, Special Functions and Applications. In honor to Richard Askey, in production, Sep. 2026
  2. Orthogonality of the big \(-1\) Jacobi polynomials for non-standard parameters ||
    Cohl, H. S. and Costas-Santos, R. S. Contemporary Mathematics 819, Applications and \(q\)-Extensions of Hypergeometric Functions, Amer. Math. Soc., Providence, RI, Eds: Howard S. Cohl, Roberto S. Costas-Santos and Robert S. Maier, 221— 231, in production, 2025
  3. Applications and \(q\)-Extensions of Hypergeometric Functions ||
    Eds: Howard S. Cohl, Roberto S. Costas-Santos and Robert S. Maier, Contemporary Mathematics 819, Amer. Math. Soc., Providence, RI, pp. xiiii+299, 2025
  4. The Laguerre constellation of classical orthogonal Polynomials || 16/01/2025 | WoS: 001404373600001
    Costas-Santos, R. S. Mathematics 13, no. 2 (2025), 277
  5. Double summation addition theorems for Jacobi functions of the first and second kind ||
    Cohl, H. S., L. Durand, C. Montoya and G. Ólafsson, Contemporary Mathematics 818, Classical Hypergeometric Functions and Generalizations, Amer. Math. Soc., Providence, RI, Eds: Howard S. Cohl, Roberto S. Costas-Santos and Robert S. Maier, 25—70, 2025
  6. Classical Hypergeometric Functions and Generalizations ||
    Eds: Cohl, H. S., Roberto S. Costas-Santos and Robert S. Maier, Contemporary Mathematics 818, Amer. Math. Soc., Providence, RI, pp. xi+288, 2025
  7. Investigating Multidimensional Degenerate Hybrid Special Polynomials and Their Connection to Appell Sequences: Properties and Applications || 7/12/2024 | WoS: 001384239000001
    Alqahtani, A. M., Yousuf, S., Wani S. A. and Costas-Santos, R. S. Axioms 13, no. 12 (2024), 859
  8. On polar Jacobi polynomials || 06/09/2024 | WoS: 001310904300001
    Costas-Santos, R. S. Mathematics 12, no. 14 (2024), 2767
  9. Multi-integral representations for Jacobi functions of the first and second kind || 5/10/2023
    Cohl, H. S. and Costas-Santos, R. S. Arab Journal of Basic and Applied Sciences 30, no. 1 (2023), 583 — 592
  10. Sobolev orthogonal polynomials: Connection formulae // 23/12/2022 / n/a
    Costas-Santos, R. S. Redel. Revista Granmense de Desarrollo Local 6, no. 4 (2022), 25 — 34
  11. Integral representations for a generalized Hermite linear functional || 22/07/2023 | WoS: 001071446500001
    Costas-Santos, R. S. Mathematics 11, no. 14 (2023), 3227
  12. Localization of zeros of polar polynomials on the unit disk || 27/08/2024 | WoS: 001303340300006
    Costas-Santos, R. S. and Rehouma, A. Rocky Mountain Journal of Mathematics 54, no. 4 (2024), 995 — 1004
  13. Nonterminating transformations and summations associated with some \(q\)-Mellin--Barnes integrals || 01/06/2023 | WoS: 000952717000001
    Cohl, H. S. and Costas-Santos, R. S. Advances in Applied Mathematics 147 (2023), 102517
  14. Symmetry of terminating series representations of the Askey-Wilson polynomials | 01/01/2023 | WoS: 000859426700003
    Cohl, H. S. and Costas-Santos, R. S. Journal of Mathematical Analysis and Applications 517, no. 1 (2023), 15 pages
  15. On polynomials orthogonal with respect to an inner product involving higher order differences. The Meixner case | H | 06/06/2022 | WoS: 000808863100001
    Costas-Santos, R. S., Soria-Lorente, A. and Vilaire J.-M. Mathematics 10, no. 11 (2022), 1952
  16. Generalizations of generating functions for basic hypergeometric orthogonal polynomials // 19/11/2022 / n/a
    Cohl, H. S., Costas-Santos, R. S., Hwang, P. R. and Wakhare, T. V . Open Journal of Mathematical Sciences 6, no. 1 (2022), 248 — 261
  17. On the relation between Gegenbauer polynomials and the Ferrers function of the first kind | 30/03/2022 | WoS: 000775954200003
    Cohl, H. S., Costas-Santos, R. S. Analysis Mathematica 48, no. 3 (2022), 695— 716
  18. Utility of integral representations for basic hypergeometric functions and orthogonal polynomials | 23/06/2022 | WoS: 000814913900001
    Cohl, H. S., Costas-Santos, R. S. The Ramanujan Journal. Special Issue in Memory of Richard Askey. Volume 61 (2022), 649—674
  19. Correction: Terminating Basic Hypergeometric Representations and Transformations for the Askey-Wilson Polynomials | 21/12/2020 | WoS: 000602409200001
    Cohl, H.S.; Costas-Santos, R.S.; Ge, L. Symmetry 12, no. 8 (2020), 1290. Symmetry 12, no. 12, (2020), 2120
  20. Multi-integral representations for associated Legendre and Ferrers functions | 25/09/2020 | WoS: 000586979700001
    Cohl, H. S., Costas-Santos, R. S. Symmetry 12, no. 10, 1598 (2020), 1 — 22
  21. Terminating basic hypergeometric representations and transformations for the Askey-Wilson polynomials | 03/08/2020 | WoS: 000567119000001
    Cohl, H. S., Costas-Santos, R. S., and Ge, L. Symmetry 12, no. 8 (2020), 1290
  22. On a generalization of the Rogers generating function | 15/12/2019 | WoS: 000465168900001
    Cohl, H. S., Costas-Santos, R. S., and Wakhare, T. V. Journal of Mathematical Analysis and Applications 475, no. 2 (2019), 1019 — 1043
  23. Some generating functions for \(q\)-polynomials | 16/12/18 | WoS: 000454725100096
    Cohl, H. S., Costas-Santos, R. S., and Wakhare, T. V. Symmetry 10, no. 12 (2018), 300 — 311
  24. Analytic properties of some basic hypergeometric-Sobolev-type orthogonal polynomials | H | 02/11/18 | WoS: 000452176500001
    Costas-Santos, Roberto S. and Soria-Lorente, A. Journal of Difference Equations and Applications 24, no. 11 (2018), 1715 — 1733
  25. The orthogonality of Al-Salam-Carlitz polynomials for complex parameters | n/a
    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.
  26. The power collection method for connection relations: Meixner polynomials | n/a
    Baeder, M. A.; Cohl, H. S., Costas-Santos, R. S. and Xu, W. Journal of Classical Analysis Volume 11, no. 2 (2017), 107 — 128
  27. Matrices Totally Positive Relative to a Tree, II | 15/09/2016 | WoS: 000378464500001
    Costas-Santos, R. S. and Johnson, C. R. Linear Algebra and its Applications 505 (2016), 1 — 10
  28. Zeros of polynomials orthogonal with respect to a signed weight | 01/03/2012 | WoS: 000300811300004
    Atia, M. J.; Benabdallah, M. and Costas-Santos, R. S. Indagationes Mathematicae 23 no. 1-2 (2012), 26 — 31
  29. The complementary polynomials and the Rodrigues operator of classical orthogonal polynomials | 01/10/2012 | WoS: 000309487600016
    Costas-Santos, R. S. and Marcellan, F. Proceedings of the American Mathematical Society 140, no. 10 (2012), 3485 — 3493
  30. Orthogonality of \(q\)-polynomials for non-standard parameters | H | 01/09/2011 | WoS: 000294143300013
    Costas-Santos, R. S. and Sanchez-Lara, J. F. Journal of Approximation Theory 163, no. 9 (2011), 1246 — 1268
  31. The Semiclassical-Sobolev orthogonal polynomials: A general approach | H | 01/01/2011 | WoS: 000285857600006
    Costas-Santos, R. S. and Moreno Balcazar, J. J. Journal of Approximation Theory 163, no. 1 (2011), 65 — 83
  32. \(q\)-Classical orthogonal polynomial: A general difference calculus approach | H | 01/07/2010 | WoS: 000278572500009
    Costas-Santos, R. S. and Marcellan, F. Acta Applicandae Mathematicae 111 (2010), 107 — 128
  33. Extensions of discrete classical orthogonal polynomials beyond the orthogonality | H | 15/03/2009 | WoS: 000263986100012
    Costas-Santos, R. S. and Sanchez-Lara, J. F. Journal of Computational and Applied Mathematics 225, no. 2 (2009), 440 — 451
  34. On the elementary symmetric functions of a sum of matrices | H | 24/08/2009 | n/a
    Costas-Santos, R. S. JP Journal of Algebra, Number Theory: Advances and Applications 1, no. 2 (2009), 99 — 112
  35. Matrices Totally Positive Relative to a Tree | H | 01/04/2009 | WoS: 000265108300001
    Johnson, C. R.; Costas-Santos, R. S. and Tadchiev, B. Electronic Journal of Linear Algebra 18 (2009), 211 — 221
  36. Second structure relation for \(q\)-semiclassical polynomials of the Hahn Tableau | H | 01/05/2007 | WoS: 000244462500014
    Marcellan, F. and Costas-Santos, R. S. Journal of Mathematical Analysis and Applications 329, no. 1 (2007), 206 — 228
  37. Factorization of the hypergeometric-type difference equation on the uniform lattice | H | 01/01/2007 | WoS: 000252984700005
    Álvarez-Nodarse, R.; Atakishiyev, N. M. and Costas-Santos, R. S. Electronic Transactions on Numerical Analysis 27 (2007), 34 — 50
  38. Limit relations between \(q\)-Krall type orthogonal polynomials | H | 01/10/2006 | WoS: 000238983700014
    Álvarez-Nodarse, R. and Costas-Santos, R. S. Journal of Mathematical Analysis and Applications 322, no. 1 (2006), 158 — 176
  39. A \(q\)-analog of the Racah polynomials and \(q\)-algebra SU\(q\)(2) in quantum optics | 01/01/06 | WoS: 000237744100001
    Álvarez-Nodarse, R.; Costas-Santos, R. S. and Smirnov, Y. F. Journal of Russian Laser Research Volume 27, Number 1 (January 2006), 1 — 32
  40. Principal minor sums of \((A+tB)^{m}\) | 18/08/05 | WoS: 000233328400016
    Johnson, C. R.; Leichenauer, S.; MacNamara, P. R. W. and Costas, R. Linear Algebra and its Applications 411 (2005), 386 — 389
  41. Factorization of the hypergeometric-type difference equation on non-uniform lattices: dynamical algebra | 08/12/2004 | WoS: 000226648800014
    Álvarez-Nodarse, R.; Atakishiyev, N. M. and Costas-Santos, R. S. Journal of Physics A: Mathematical and General 38, no. 1 (2005), 153 — 174
  42. Factorization method for difference equations of hypergeometric type on nonuniform lattices | 29/06/01 | WoS: 000170241400006
    Álvarez-Nodarse, R. and Costas-Santos, R. S. Journal of Physics A: Mathematical and General volume 34, no. 27 (2001), 5551 — 5569