Orthogonal harmonic polynomials on U(2) (Q1092354)

This paper, based on physical motivation, concernes with the polynomial solutions of the differential equation \[ (1-x^ 2)x^ 2y''+(1-x^ 2)xy'-m^ 2y+\omega^ 2x^ 2y=0, \] where m is an integer. These polynomial solutions \(y_{n,k}\), \(k=1,2,...\), are associated to the values \(2k+m\) of the parameteer \(\omega\) and are related to the Jacobi polynomials. Their properties, as Rodrigues formula and generating function for the case \(m=0\), product decomposition, asymptotic representations and completeness, are presented in detail.