[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]
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关于无穷区间(-∞,+∞)上的S.Bernstein多项式的推广形式()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
18
期数:
1988年第5期
页码:
134-138
栏目:
本刊信息
出版日期:
1988-09-20

文章信息/Info

Title:
On a Regarding Generalization of S. Bernstein’s Polynomial to the Two-sided Infinite Interval
作者:
蔡冠华
南京工学院数学力学系
Author(s):
Cai Guanhua(Department of Mathematics and Mechanics)
关键词:
S. Bernstein’s polynomials degree of approximation even function odd function
Keywords:
S. Bernstein’s polynomials degree of approximation even function odd function
分类号:
+
DOI:
10.3969/j.issn.1001-0505.1988.05.019
摘要:
<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.
更新日期/Last Update: 2013-04-30