The quasi-orthogonality of the derivatives of semi-classical polynomials
The distributional equation of a semi-classical functional provides an efficient way to study the properties of the semi-classical OPS/functionals. A particular case of semi-classical OPS/functionals are the classical ones, when a regularity condition holds for the distributional equation. It was shown earlier by the author that in general such condition does not hold. The main goal of the present paper is to analyze the consequences of the failure of regularity in the quasi-orthogonality of the derivatives of the semi-classical OPS. This study leads the author to the coprimality condition.
semi-classical functionals and orthogonal polynomials
scientific article; zbMATH DE number 1893651