Uniform asymptotic formula for orthogonal polynomials with exponential weight

Let {p(n) (x)}(n greater than or equal to 0) be the set of orthonormal poly nomials with respect to the exponential weight w (x) = e(-v(x)), where v (x ) = x(2m) + ... is a monic polynomial of degree 2 m with m greater than or equal to 2 and is even. An asymptotic approximation is obtained for p(n)(x) , as n --> infinity, which holds uniformly for 0 less than or equal to x le ss than or equal to O(n(1/2m)). As a corollary, a three-term asymptotic exp ansion is also derived for the zeros of these polynomials.