Properties of some finite families of classical orthogonal polynomials

This paper looks at various groups of new families of orthogonal polynomials that were defined in the last two decades. We show that they are intimately related to known systems so that they are not really new and some of their properties can be determined from known results. In particular, we derive a new hypergeometric representation of a large polynomial family defined by M. Masjed-Jamei (2004) and we show that these polynomials can be written in terms of the Jacobi polynomials with complex parameters. We derive new properties of these polynomials including their three-term recurrence relation, structure relations, moments, connection coefficients and linearization coefficients that were not given in the original paper although the method used to derive them are not new.