Asymptotic properties of generalized Laguerre orthogonal polynomials. (Q1890420)

The Laguerre polynomials considered in this paper are orthogonal with respect to a Sobolev inner product. New asymptotic properties of these polynomials are given, together with a limit relation between the zeros of the polynomials and the zeros of a Bessel function. The results are obtained by writing the generalized polynomials as a sum of three classical Laguerre polynomials. Numerical examples illustrate the approximations of the zeros.