Abstract
Letpn(x) denote the orthogonal polynomials associated with the Freud weight exp(−x4),x∈R. Letx=(4n/3)1/4w. An asymptotic approximation is constructed forpn(x), which holds uniformly for −1+ε⩽w⩽M, where 0<ε<1 and 1<M<∞. This approximation involves the Airy function and its derivative, and it includes the two asymptotic formulas previously obtained by P. Nevai. Also presented is a four-term asymptotic expansion for the zeros ofpn(x).
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