𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Asymptotics of Diagonal Hermite–Padé Approximants toez

✍ Scribed by F. Wielonsky

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
348 KB
Volume
90
Category
Article
ISSN
0021-9045

No coin nor oath required. For personal study only.

✦ Synopsis

Let m be a fixed positive integer. We consider Hermite Pade approximants to the exponential function

where the degree of the polynomials A p , 0 p m, is less than n. As n Ä , 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 Pade approximants asymptotically minimize exponential polynomials of the above form on a disk [ |z| ], provided \ does not exceed ?Âm. These results generalize some of those obtained by Borwein (Const. Approx. 2 (1986), 291 302) on quadratic Hermite Pade approximants.

1997 Academic Press Mahler [10] showed that they could also be used to prove the transcendence of e. These two types of Hermite Pade approximants, explicitly article no. AT963081 283

📜 SIMILAR VOLUMES

On Polynomials Related with Hermite–Padé
On Polynomials Related with Hermite–Padé Approximations to the Exponential Function
✍ Kathy A. Driver; Nico M. Temme 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 445 KB

We investigate the polynomials P n , Q m , and R s , having degrees n, m, and s, respectively, with P n monic, that solve the approximation problem We give a connection between the coefficients of each of the polynomials P n , Q m , and R s and certain hypergeometric functions, which leads to a sim

Convergence Rates of Padé and Padé-Type
Convergence Rates of Padé and Padé-Type Approximants
✍ Amiran Ambroladze; Hans Wallin 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 356 KB

A comparison is made between Pade and Pade -type approximants. Let Q n be the n th orthonormal polynomial with respect to a positive measure + with compact support in C. We show that for functions of the form where w is an analytic function on the support of +, Pade -type approximants with denomina

Padé approximation of Stieltjes series
Padé approximation of Stieltjes series
✍ G.D Allen; C.K Chui; W.R Madych; F.J Narcowich; P.W Smith 📂 Article 📅 1975 🏛 Elsevier Science 🌐 English ⚖ 627 KB