MONOTONICITY AND ASYMPTOTICS OF ZEROS OF LAGUERRE-SOBOLEV-TYPE ORTHOGONAL POLYNOMIALS OF HIGHER ORDER DERIVATIVES

In this paper we analyze the location of the zeros of polynomials orthogonal with respect to the inner product (0.1) < p,q > = integral(infinity)(0) p(x)q(s)x(alpha)e(-x)dx + Np((j))(0)q((j))(0), where alpha > -1, N >= 0, and j is an element of N. In particular, we focus our attention on their interlacing properties with respect to the zeros of Laguerre polynomials as well as on the monotonicity of each individual zero in terms of the mass N. Finally, we give necessary and sufficient conditions in terms of N in order for the least zero of any Laguerre-Sobolev-type orthogonal polynomial to be negative.