Uniform asymptotic formula for orthogonal polynomials with exponential weight

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

12 Scopus Citations
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Author(s)

  • W. Y. Qiu
  • R. Wong

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)992-1029
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume31
Issue number5
Publication statusPublished - Apr 2000

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.

Research Area(s)

  • Exponential weight, Orthogonal polynomials, Turning point, Uniform asymptotic approximation, Zeros

Citation Format(s)

Uniform asymptotic formula for orthogonal polynomials with exponential weight. / Qiu, W. Y.; Wong, R.
In: SIAM Journal on Mathematical Analysis, Vol. 31, No. 5, 04.2000, p. 992-1029.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review