@article{f7694a496f684a9daa4c5c60060de566, title = "Uniform asymptotic formula for orthogonal polynomials with exponential weight", abstract = "Let {pn(x)}n≥0 be the set of orthonormal polynomials with respect to the exponential weight w(x) = e-v(x), where v(x) = x2m + ⋯ is a monic polynomial of degree 2m with m ≥ 2 and is even. An asymptotic approximation is obtained for pn(x), as n → ∞, which holds uniformly for 0 ≤ x ≤ O(n1/2m. As a corollary, a three-term asymptotic expansion is also derived for the zeros of these polynomials.", keywords = "Exponential weight, Orthogonal polynomials, Turning point, Uniform asymptotic approximation, Zeros", author = "Qiu, {W. Y.} and R. Wong", year = "2000", month = apr, doi = "10.1137/S0036141098344671", language = "English", volume = "31", pages = "992--1029", journal = "SIAM Journal on Mathematical Analysis", issn = "0036-1410", publisher = "Society for Industrial and Applied Mathematics", number = "5", }