Weighted Zero Distribution for Polynomials Orthogonal on an Infinite Interval

The distribution of the zeros of orthogonal polynomials on an infinite interval is studied by means of a distribution function $Z_n $ that makes a jump at each zero of the nth polynomial. The jumps are chosen properly in order that the function $Z_n $ converges as $n \to \infty $. The asymptotic behaviour is given for the special case of (generalized) Laguerre and Hermite polynomials.