The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients

@inproceedings{Kuijlaars1997TheAZ,
  title={The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients},
  author={Arno B. J. Kuijlaars and Walter Van Assche},
  year={1997}
}
We study the zeros of orthogonal polynomials pn,N , n = 0, 1, . . ., that are generated by recurrence coefficients an,N and bn,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 that the polynomials pn,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… CONTINUE READING