4 papers · 1 filter
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]…