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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_…
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…