A Class of Orthogonal Polynomials on the Radial Rays in the Complex Plane

We introduce a class of polynomials orthogonal on some radial rays in the complex plane and investigate their existence and uniqueness. A recurrence relation for these polynomials, a representation, and the connection with standard polynomials orthogonal on 0, 1.are derived. It is shown that their zeros are simple and distributed symmetrically on the radial rays, with the possible exception of a multiple zero at the origin. An analogue of the Jacobi polynomials and the corresponding problem with the generalized Laguerre polynomials are also treated.