  We construct two families of orthogonal polynomials associated with the
universal central extensions of the superelliptic Lie algebras. These
polynomials satisfy certain fourth order linear differential equations, and one
of the families is a particular collection of associated ultraspherical
polynomials. We show that the generating functions of the polynomials satisfy
fourth order linear PDEs. Since these generating function can be represented by
superelliptic integrals, we have examples of linear PDEs of fourth order with
explicit solutions without complete integrability.
