The paper is devoted to construct an asymptotic approximation for the orthogonal polynomials , associated with the Freud weight , . The following theorem extends a result of Nevai.
Theorem: Let and be fixed, and let and . Then the asymptotic formula
holds uniformly for , , where
and is the Airy function. Moreover, when , the uniform asymptotic formula (1) holds for . Let . The following result is proved for the positive zeros of the polynomial
where is the th negative zero of the Airy function .