On certain special sets of orthogonal polynomials

Pollaczek has introduced certain sets of orthogonal polynomials with remarkableproperties.In the present paper we are considering primarily the polynomials introduced in the first note, the others being certain generalizations.In view of their relatively simple definition, these polynomials can readily be studied.They serve as illustrations for certain "irregular" phenomena in the theory of orthogonal polynomials.Extensions of the well known integral representations (integrals of Laplace and Mehler) and of other formal properties will be discussed at a later opportunity.