arXiv subjects

X. -S. Wang

Publications and source records attributed to X. -S. Wang.

3 recordsLinked to original sources

arXiv2011

Global Asymptotics of the Meixner Polynomials

Using the steepest descent method for oscillatory Riemann-Hilbert problems introduced by Deift and Zhou [Ann. Math. {\bf 137}(1993), 295-368], we derive asymptotic formulas for the Meixner polynomials in two regions of the complex plane separated by the boundary of a rectangle. The asymptotic formula on the boundary of the rectangle is obtained by taking limits from either inside or outside. Our results agree with the ones obtained earlier for $z$ on the positive real line by using the steepest descent method for integrals [Constr. Approx. {\bf 14}(1998), 113-150].

math.CA↗

arXiv2011

Asymptotics of Orthogonal Polynomials via Recurrence Relations

We use the Legendre polynomials and the Hermite polynomials as two examples to illustrate a simple and systematic technique on deriving asymptotic formulas for orthogonal polynomials via recurrence relations. Another application of this technique is to provide a solution to a problem recently raised by M. E. H. Ismail.

math.CA↗

arXiv2009

Uniform Asymptotics of the Meixner Polynomials

Using the steepest descent method of Deift-Zhou, we derive locally uniform asymptotic formulas for the Meixner polynomials. These include an asymptotic formula in a neighborhood of the origin, a result which as far as we are aware has not yet been obtained previously. This particular formula involves a special function, which is the uniformly bounded solution to a scalar Riemann-Hilbert problem, and which is asymptotically (as the polynomial degree $n$ tends to infinity) equal to the constant $"1"$ except at the origin. Numerical computation by using our formulas, and comparison with earlier results, are also given.

math.CA↗