# [1]蔡冠华.关于无穷区间(-∞,+∞)上的S.Bernstein多项式的推广形式[J].东南大学学报(自然科学版),1988,18(5):134-138.[doi:10.3969/j.issn.1001-0505.1988.05.019] 　Cai Guanhua(Department of Mathematics and Mechanics).On a Regarding Generalization of S. Bernstein’s Polynomial to the Two-sided Infinite Interval[J].Journal of Southeast University (Natural Science Edition),1988,18(5):134-138.[doi:10.3969/j.issn.1001-0505.1988.05.019] 点击复制 关于无穷区间(-∞,+∞)上的S.Bernstein多项式的推广形式() 分享到： var jiathis_config = { data_track_clickback: true };

18

1988年第5期

134-138

1988-09-20

## 文章信息/Info

Title:
On a Regarding Generalization of S. Bernstein’s Polynomial to the Two-sided Infinite Interval

Author(s):
Cai Guanhua(Department of Mathematics and Mechanics)

Keywords:

+
DOI:
10.3969/j.issn.1001-0505.1988.05.019

<正> 设f（x）是定义在[0,+∞)上的函数,吴华英引进了S. Bernstein多项式推广的另一种形式: B_n^*（f, x）=e^{-（nx）^{2}} sum from n=k=0 to ∞ f(k^{1/2}/n)（nx）^{2l}/k!它不同于O. Szasz提示的S. Bernstein多项式在无穷区间的推广形式 B_n（f, x）=e^{-nx} sum from n=k=0 to ∞ f（k/n）（nx）^k/k! 以上两种形式都是[0,+∞)上的推广。本文将函数f（x）定义在（-∞,+∞）上,并给出它的推广形式:
Abstract:
This paper proposes a generalization of S. Bernstein’s polynomials in the interval (-∞,+∞), and gives an estimation of accuracy of the approximation.