Asymptotics of diagonal Hermite-Pade approximants to e(z)

[摘要] Let m be a fixed positive integer. We consider Hermite-Pade approximants to the exponential function [GRAPHICS] where the degree of the polynomials A(p), 0 less than or equal to p less than or equal to m, is less than n. As n --> infinity, exact asymptotics for the A(p)'s and the remainder term R, along with an upper bound on the zeros of the polynomials A(p), are given. These asymptotics show that shifted Hermite-Padi approximants asymptotically minimize exponential polynomials of the above form on a disk {\z\ less than or equal to rho}, provided rho does not exceed pi/m. These results generalize some of those obtained by Borwein (Const. Approx. 2 (1986), 291-302) on quadratic Hermite-Padi approximants. (C) 1997 Academic Press.

[发布日期] 1997-08-01