14 papers
On classical orthogonal polynomials on bi-lattices
K. Castillo, G. Filipuk, D. Mbouna
In [J. Phys. A: Math. Theor. 45 (2012)], while looking for spin chains that admit perfect state transfer, Vinet and Zhedanov found an apparently new sequence of orthogonal polynomi…
Epilegomena to the study of semiclassical orthogonal polynomials
K. Castillo, D. Mbouna
In his monograph [Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, 2005 (paperback edition 2009)], Ismail conjectured that certain structur…
Remarks on the paper "Recurrence equations and their classical orthogonal polynomial solutions on a quadratic or a q-quadratic lattice"
D. Mbouna
We provide a simple method to recognize classical orthogonal polynomials on lattices defined only by their coefficients of the three term recurrence relation.
Coherent pair of measures for orthogonal polynomials on lattices
D. Mbouna
We consider two sequences of orthogonal polynomials and with respect regular functionals and , respectively. We assume that $…
On classical orthogonal polynomials on lattices and some characterization theorems
K. Castillo, D. Mbouna, J. Petronilho
In this chapter are given necessary and sufficient conditions for the regularity of solutions of the functional equation appearing in the theory of classical orthogonal polynomials…
A counterexample to a conjecture of M. Ismail
K. Castillo, D. Mbouna
In an earlier work [K. Castillo et al., J. Math. Anal. Appl., 514 (2022) 126358], we give positive answer to the first, and apparently more easy, part of a conjecture of M. Ismail…
Characterization of Orthogonal Polynomials on lattices
D. Mbouna, Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar
We consider two sequences of orthogonal polynomials and such that $$ \sum_{j=1} ^{M} a_{j,n}\mathrm{S}_x\mathrm{D}_x ^k P_{k+n-j} (z)=\sum_{j=1}…
Proof of two conjectures on Askey-Wilson polynomials
K. Castillo, D. Mbouna
We give positive answer to two conjectures posed by M. E. H Ismail in his monograph [Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, 2005]…
A characterization of continuous -Jacobi, Chebyshev of the first kind and Al-Salam Chihara polynomials
K. Castillo, D. Mbouna, J. Petronilho
The purpose of this note is to characterize those orthogonal polynomials sequences for which $$ π(x)\mathcal{D}_q P_n(x)=(a_n x+b_n)P_n(x)+c_n P_{n-1}(x),\quad n=0…
Remarks on Askey-Wilson polynomials and Meixner polynomials of the second kind
K. Castillo, D. Mbouna, J. Petronilho
The purpose of this note is twofold: firstly to characterize all the sequences of orthogonal polynomials such that $$ \frac{\triangle}{{\bf \triangle} x(s-1/2)}P_…
On the functional equation for classical orthogonal polynomials on lattices
K. Castillo, D. Mbouna, J. Petronilho
Necessary and sufficient conditions for the regularity of solutions of the functional equation appearing in the theory of classical orthogonal polynomials on lattices are stated. M…
On discrete coherent pairs of measures
R. Álvarez-Nodarse, K. Castillo, D. Mbouna +1
In [Castillo \& Mbouna, Indag. Math. {\bf 31} (2020) 223-234], the concept of -coherent pairs of order with index is introduced. This definition, implicitly relate…
On classical orthogonal polynomials related to Hahn's operator
R. Álvarez-Nodarse, K. Castillo, D. Mbouna +1
Let be a nonzero linear functional acting on the space of polynomials. Let be a Hahn operator acting on the dual space of polynomials. Suppose that the…
On another extension of coherent pairs of measures
K. Castillo, D. Mbouna
Let and be fixed non-negative integer numbers and let be a polynomial of degree . Suppose that and are two orthogonal polynomial…