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      On linearly related sequences of difference derivatives of discrete orthogonal polynomials  [Article]

      Álvarez Nodarse, Renato; Soares Petronilho, José Carlos; Pinzón Cortés, Natalia Camila; Sevinik Adigüzel, Rezan (Elsevier, 2015-08-15)
      Let ν be either ω ∈ C \ {0} or q ∈ C \ {0, 1}, and let Dν be the corresponding difference operator defined in the usual way either by Dωp(x) = p(x+ω)−p(x) ω or Dqp(x) = p(qx)−p(x) (q−1)x. Let U and V be two moment regular ...
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      On the generalized Askey-Wilson polynomials  [Article]

      Álvarez Nodarse, Renato; Sevinik Adigüzel, Rezan (Elsevier, 2013-06)
      In this paper a generalization of Askey-Wilson polynomials is introduced. These polynomials are obtained from the Askey-Wilson polynomials via the addition of two mass points to the weight function of them at the points ...
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      On the Krall-type polynomials on q-quadratic lattices  [Article]

      Álvarez Nodarse, Renato; Sevinik Adigüzel, Rezan (Elsevier, 2011-08)
      In this paper, we study the Krall-type polynomials on non-uniform lattices. For these polynomials the second order linear difference equation, q-basic series representation and three-term recurrence relations are obtained. ...
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      On the limit of non-standard q-Racah polynomials  [Article]

      Álvarez Nodarse, Renato; Sevinik Adigüzel, Rezan (2014-03-15)
      The aim of this article is to study the limit transitions from non-standard q-Racah polynomials to big q-Jacobi, dual q-Hahn, and q-Hahn polynomials such that the orthogonality properties and the three-term recurrence ...
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      The q-Racah-Krall-type polynomials  [Article]

      Álvarez Nodarse, Renato; Sevinik Adigüzel, Rezan (Elsevier, 2012-08-01)
      In this paper the Krall-type polynomials obtained via the addition of two mass points to the weight function of the standard q-Racah polynomials are introduced. Several algebraic properties of these polynomials are obtained ...