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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. 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. Semiclassical quasi-orthogonal polynomials. A general difference calculus approach (with F Marcellan)
  6. The orthogonality of the $q$-Laguerre for a general parameter (with F Marcellan)
  7. Generating functions of Classical polynomials satisfying Laguerre-type Second structure relation (with J F Mañas-Mañas, J J Moreno-Balcazar)
  8. Algebraic and orthogonality properties of someq-analogs of the Laguerre polynomials for non classical parameters (with M T Perez, M Piñar)
  9. On polynomials defined by a modified Rodrigues formula (with F Marcellan)
  10. Zeros of Krawtchouk Sobolev-type Orthogonal polynomials. A numerical study (With A Soria Lorente)
  11. Zeros of Al-Salam-Carlitz polynomials. The real parameters case

Preprints

  1. The Laguerre-type Classical Orthogonal Polynomials | [Arx] | 2024
  2. The \(\xi\)−Laguerre polynomials | [Arx] | 2024
  3. Localization of zeros of polar Jacobi polynomials | [Arx] | 2024
  4. The permanent of a sum of matrices | [Arx] | 2024
  5. Spectra of Tridiagonal Matrices over a Field (with C R Johnson) | Submitted to Arab Journal of Basic and Applied Sciences, 2024 | [Arx]
  6. Classical exceptional orthogonal polynomials: a global overview (With J S Kelly) | Submitted to Bulletin des sciences mathématiques, 2024 | [Arx]
  7. Double summation addition theorems for Jacobi functions of the first and second kind (With H S Cohl, L. Durand, C. Montoya and G. Ólafsson) | Submitted to CONM proceedings, 2024 | [Arx]

Papers

  1. Special values for continuous \(q\)-Jacobi polynomials ||
    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. Accepted, 2023
  2. Orthogonality of the big \(-1\) Jacobi polynomials for non-standard parameters ||
    Cohl, H. S. and Costas-Santos, R. S. AMS Contemporary Mathematics Proceedings on Hypergeometric Functions, q-series and Applications. Accepted, 2023
  3. 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 (1) (2023), 583 — 592
  4. 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
  5. Integral representations for a generalized Hermite linear functional || 22/07/2023 | WoS: 001071446500001
    Costas-Santos, R. S. Mathematics 11 no. 14 (2023), 3227
  6. Localization of zeros of polar polynomials on the unit disk ||
    Costas-Santos, R. S. and Rehouma, A. Rocky Mountain Journal of Mathematics. Accepted, 2023
  7. 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
  8. 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
  9. On polynomials orthogonal with respect to an inner product involving higher order differences. The Meixner case | 06/06/2022 - WoS: 000808863100001
    Costas-Santos, R. S., Soria-Lorente, A. and Vilaire J.-M. Mathematics 10 no. 11 (2022), 1952
  10. 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
  11. 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
  12. 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 (2023), 649—674
  13. 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 2020, 12, 1290. Symmetry 12 (12), 2120 (2020), 2 pages.
  14. 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
  15. 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
  16. 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
  17. 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
  18. Analytic properties of some basic hypergeometric-Sobolev-type orthogonal polynomials | 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
  19. 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.
  20. 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
  21. 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
  22. 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
  23. 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
  24. Orthogonality of q-polynomials for non-standard parameters | 01/09/2011 | WoS: 000294143300013
    Costas-Santos, R. S. and Sanchez-Lara, J. F. Journal of Approximation Theory 163, no. 9 (2011), 1246 — 1268
  25. The Semiclassical-Sobolev orthogonal polynomials: A general approach | 01/01/2011 | WoS: 000285857600006
    Costas-Santos, R. S. and Moreno Balcazar, J. J. Journal of Approximation Theory 163, no. 1 (2011), 65 — 83
  26. q-Classical orthogonal polynomial: A general difference calculus approach | 01/07/2010 | WoS: 000278572500009
    Costas-Santos, R. S.and Marcellan, F. Acta Applicandae Mathematicae 111 (2010), 107 — 128
  27. Extensions of discrete classical orthogonal polynomials beyond the orthogonality | 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
  28. On the elementary symmetric functions of a sum of matrices | 24/08/2009 | n/a
    Costas-Santos, R. S. JP Journal of Algebra, Number Theory: Advances and Applications1, No. 2 (2009), 99 — 112
  29. Matrices Totally Positive Relative to a Tree | 01/04/2009 | WoS: 000265108300001
    Johnson, C. R.; Costas-Santos, R. S. and Tadchiev, B. Electronic Journal of Linear Algebra 18 (2009), 211 — 221
  30. Second structure relation for q-semiclassical polynomials of the Hahn Tableau | 01/05/2007 | WoS: 000244462500014
    Marcellan, F. and Costas-Santos, R. S. Journal of Mathematical Analysis and Applications 329, no. 1 (2007), 206 — 228
  31. Factorization of the hypergeometric-type difference equation on the uniform lattice | 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
  32. Limit relations between q-Krall type orthogonal polynomials | 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
  33. A q-analog of the Racah polynomials and q-algebra SUq(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
  34. 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
  35. 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
  36. 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