Semi classical orthogonal polynomials on nonuniform
lattices with respect to a linear functional
L are defined as polynomials
(Pn) where the degree of
Pn is exactly
n , the
Pn satisfy the orthogonality relation
and
L satisfies the Pearson equation
where
ϕ is a non zero polynomial and
ψ a polynomial of degree at least 1. In this work, we prove that the multiplication of semi classical linear functional by a first degree polynomial, the addition of a Dirac measure to the semi-classical regular linear functional on nonuniform
lattice give semi classical linear functional but not necessary of the same class. We apply these modifications to some classical orthogonal polynomials.