LAUSR

Abstract Semi classical orthogonal polynomials on nonuniform lattices with respect to a linear functional L are defined as polynomials ( P n ) where the degree of P n is exactly n, the P n satisfy the orthogonality relation 〈 L , P n P m 〉 = 0 , n ≠ m , 〈 L , P n P n 〉 ≠ 0 , n ≥ 0 and L satisfies the Pearson equation D x ( ϕ L ) = S x ( ψ L ) , 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.