Uniform asymptotics of the Stieltjes-Wigert polynomials via the Riemann-Hilbert approach
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
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Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 698-718 |
| Journal / Publication | Journal des Mathematiques Pures et Appliquees |
| Volume | 85 |
| Issue number | 5 |
| Publication status | Published - May 2006 |
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Abstract
It has been known for some time that the existing asymptotic methods for integrals and differential equations are not applicable in the case of Stieltjes-Wigert polynomials with degree going to infinity. Using the recently introduced nonlinear steepest descent method for Riemann-Hilbert problems, here we not only derive an asymptotic expansion for these polynomials, but we also show that the result holds uniformly in the complex plane except for a sector containing the real axis from -∞ to frac(1, 4). Furthermore, we give an asymptotic formula for the zeros of these polynomials, which approximates the true values of the zeros closely. © 2005 Elsevier SAS. All rights reserved.
Research Area(s)
- Logarithmic potential, Riemann-Hilbert problem, Stieltjes-Wigert polynomials, Uniform asymptotics, Zeros
Citation Format(s)
Uniform asymptotics of the Stieltjes-Wigert polynomials via the Riemann-Hilbert approach. / Wang, Z.; Wong, R.
In: Journal des Mathematiques Pures et Appliquees, Vol. 85, No. 5, 05.2006, p. 698-718.
In: Journal des Mathematiques Pures et Appliquees, Vol. 85, No. 5, 05.2006, p. 698-718.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
