  A connection between Romanovski polynomials and those polynomials that solve
the one-dimensional Schr\"odinger equation with the trigonometric Rosen-Morse
and hyperbolic Scarf potential is established. The map is constructed by
reworking the Rodrigues formula in an elementary and natural way. The
generating function is summed in closed form from which recursion relations and
addition theorems follow. Relations to some classical polynomials are also
given.
