Journal of the
Korean Mathematical Society JKMS

We investigate the asymptotic behavior of the extreme zeros of orthogonal polynomials with respect to a positive measure $d\alpha(x)$ in terms of the three term recurrence coefficients. We then show that the asymptotic behavior of extreme zeros of orthogonal polynomials with respect to $g^2(x) d\alpha(x)$ is the same as that of extreme zeros of orthogonal polynomials with respect to $d\alpha(x)$ when $g(x)$ is a polynomial with all zeros in a certain interval determined by $d\alpha(x)$. Several illustrating examples are also given.

Keywords: orthonormal polynomials, asymptotic behavior of extreme zeros

MSC numbers: 26C10, 42C05