Characterization of the D-Laguerre-Hahn orthogonal polynomials of class one via the cubic decomposition

In the present work, we deal with a monic orthogonal polynomial sequence (MOPS) deduced by its cubic decomposition (CD) W-3n(x)=P-n(x(3)), n >= 0. Our goal is to determine all D-Laguerre-Hahn strict of class one of these sequences. From the CD structure, only one family of MOPS appears in connection with the D-Laguerre-Hahn of class zero of Jacobi type in the singular case and the nonsingular one. Their recurrence coefficients are highlighted.

Automated summary

In this work, we analyzed a monic orthogonal polynomial sequence (MOPS) deduced from its cubic decomposition (CD), aiming to determine all D-Laguerre-Hahn strict of class one of these sequences. Based on the CD structure, only one family of MOPS is found to be related to the D-Laguerre-Hahn of class zero of Jacobi type in both singular and nonsingular cases. The recurrence coefficients of these sequences are highlighted.