17 papers · 1 filter
On the positivity of a certain function related with the Digamma function
K. Castillo
It is proved that for all and , which improves the result of [Al-Musallam and Bustoz in Raman…
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…
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 $$ π(x)\mathcal{D}_q P_n(x)=(a_n x+b_n)P_n(x)+c_n P_{n-1}(x),\quad n=0…
Classical orthogonal polynomials revisited
K. Castillo, J. Petronilho
This manuscript contains a small portion of the algebraic theory of orthogonal polynomials developed by Maroni and their applicability to the study and characterization of the clas…
Remarks on Askey-Wilson polynomials and Meixner polynomials of the second kind
K. Castillo, D. Mbouna, J. Petronilho
The purpose of this note is twofold: firstly to characterize all the sequences of orthogonal polynomials such that $$ \frac{\triangle}{{\bf \triangle} x(s-1/2)}P_…