Abj. Kuijlaars et W. Van Assche, The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients, J APPROX TH, 99(1), 1999, pp. 167-197
We study the zeros of orthogonal polynomials p(n, N), n = 0, 1, ..., that a
re generated by recurrence coefficients a(n, N) and b(n, N) depending on a
parameter N. Assuming that the recurrence coefficients converge whenever n,
N tend to infinity in such a way that the ratio n/N converges, we show tha
t the polynomials p(n, N) have an asymptotic zero distribution as n/N tends
to t > 0 and we present an explicit formula for the limiting measure. This
formula contains the asymptotic zero distributions for various special cla
sses of orthogonal polynomials that were found earlier by different methods
, such as Jacobi polynomials with varying parameters, discrete Chebyshev po
lynomials, Krawtchouk polynomials, and Tricomi-Carlitz polynomials. We also
give new results on zero distributions of Charlier polynomials, Stieltjes-
Wigert polynomials, and Lommel polynomials. (C) 1999 Academic Press.