Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4642696 | Journal of Computational and Applied Mathematics | 2007 | 18 Pages |
Abstract
We obtain strong and uniform asymptotics in every domain of the complex plane for the scaled polynomials a(3nz), b(3nz), and c(3nz) where a, b, and c are the type II Hermite-Padé approximants to the exponential function of respective degrees 2n+2, 2n and 2n, defined by a(z)e-z-b(z)=O(z3n+2) and a(z)ez-c(z)=O(z3n+2) as zâ0. Our analysis relies on a characterization of these polynomials in terms of a 3Ã3 matrix Riemann-Hilbert problem which, as a consequence of the famous Mahler relations, corresponds by a simple transformation to a similar Riemann-Hilbert problem for type I Hermite-Padé approximants. Due to this relation, the study that was performed in previous work, based on the Deift-Zhou steepest descent method for Riemann-Hilbert problems, can be reused to establish our present results.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
A.B.J. Kuijlaars, H. Stahl, W. Van Assche, F. Wielonsky,