Discrete semi-classical orthogonal polynominals

Abstract

Abstract Orthogonal polynominals associated with δ-semi-classical functionals will be studied as a generalization of the δ-classical functionals. The concept of class and a criterion for determining it will be given. Theδ-difference equation that the corresponding formal stieltjes series satisfies is obtained. The quasi-orthogonality property satisfied by theδ-differences of these polynomials is analysed.Two structure relations as well as a quardratic relation are obtained. The second order difference equation is determined. Keywords: Orthogonal PolynominalsQuasi-orthogonalityDifference equationsAMS Subject Classification: 33C2539A70