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In the present work, we deal with a monic orthogonal polynomial sequence (MOPS) deduced by its cubic decomposition (CD). 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.

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