RATIONAL APPROXIMATION TO EX AND TO RELATED FUNCTIONS

被引：2

作者：

NEWMAN, DJ

REDDY, AR

机构：

[1] PRINCETON UNIV,INST ADV STUDIES,PRINCETON,NJ 08540

[2] RUTGERS STATE UNIV,NEW BRUNSWICK,NJ 08903

来源：

JOURNAL OF APPROXIMATION THEORY | 1979年 / 25卷 / 01期

关键词：

D O I：

10.1016/0021-9045(79)90029-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

According to a well-known result of S. N. Bernstein, ex can be approximated uniformly on [-1, 1] by polynomials of degree ≤n with an error of the order [2n(n + 1)!]-1. In this note it is shown that the smallest (uniform norm) error in approximating ex by reciprocals of polynomials of degree ≤n is also of the order [2n(n + 1)!]-1. We denote throughout by Pn(x), Qn(x) real polynomials of degree ≤n. We show, furthermore, that the smallest error in approximating ex by rational functions of the form Pn(x) Qn(x) where the coefficients of Qn are ≥0 is again of that same order. © 1979.

引用

页码：21 / 30

页数：10