Global asymptotics of hermite polynomials via Riemann-Hilbert approach
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 661-682 |
| Journal / Publication | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 7 |
| Issue number | 3 |
| Publication status | Published - May 2007 |
Link(s)
Abstract
In this paper, we study the asymptotic behavior of the Hermite polynomials Hn((2n + 1)1/2z) as n → ∞. A globally uniform asymptotic expansion is obtained for z in an unbounded region containing the right half-plane Re z ≥ 0. A corresponding expansion can also be given for z in the left half-plane by using the symmetry property of the Hermite polynomials. Our approach is based on the steepest-descent method for Riemann-Hilbert problems introduced by Deift and Zhou.
Research Area(s)
- Airy functions, Global asymptotics, Hermite polynomials, Riemann-Hilbert problems
Citation Format(s)
Global asymptotics of hermite polynomials via Riemann-Hilbert approach. / Wong, R.; Zhang, L.
In: Discrete and Continuous Dynamical Systems - Series B, Vol. 7, No. 3, 05.2007, p. 661-682.
In: Discrete and Continuous Dynamical Systems - Series B, Vol. 7, No. 3, 05.2007, p. 661-682.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
