Laurent polynomials related to the Hahn-Exton q-Bessel function, which are qanalogues of the Lommel polynomials, have been introduced by Koelink and Swarttouw. The explicit strong moment functional with respect to which the Laurent q-Lommel polynomials are orthogonal is given. The strong moment functional gives rise to two positive definite moment functionals. For the corresponding sets of orth...

An extension of symmetric classical orthogonal polynomials is d-symmetric classical d-orthogonal polynomials, d being a positive number. These polynomials and their derivatives satisfy particular (d+1)-order recurrence relations. Many works deals with these families. Our purpose is to derive some more results for this class of polynomials. In fact, in terms of hypergeometric functions, we expre...

We consider a modiication of moment functionals for some classical polynomials of a discrete variable by adding a mass point at x = 0. We obtain the resulting orthogonal polynomials, identify them as hypergeometric functions and derive the second order diierence equation which these polynomials satisfy. The corresponding tridiagonal matrices and associated polynomials were also studied. x1 Intr...

In this paper a general theory of semi-classical matrix orthogonal polynomials is developed. We define the semi-classical linear functionals by means of a distri-butional equation D(uA) = uB, where A and B are matrix polynomials. Several characterizations for these semi-classical functionals are given in terms of the corresponding (left) matrix orthogonal polynomials sequence. They involve a qu...

This paper is devoted to the study of general (Laurent) polynomial modifications of moment functionals on the unit circle, i.e., associated with hermitian Toeplitz matrices. We present a new approach which allows us to study polynomial modifications of arbitrary degree. The main objective is the characterization of the quasi-definiteness of the functionals involved in the problem in terms of a ...