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1、什么样的连续函数能由整系数多项式逼近 什么样的连续函数能由整系数多项式逼近摘要:本文主要译自1,它系统地讨论了什么样的连续函数能由整系数多项式逼近,有以下两种情形: (1)区间长度大于等于4的区间上,能由整系数多项式逼近的连续函数是这些整系数多项式本身;(2)在区间长度严格小于4的区间 上,连续函数 能被整系数多项式1致逼近当且仅当 在 插值多项式为整系数多项式.关键词:逼近;整系数多项式;插值多项式;代数整数.What Can Be Approximated by Polynomials with Integer CoefficientsAbstract: This article is m
2、ainly translated from 1.What can be approximated by polynomials with integer coefficients is given in the following two aspects:(1)If the interval has length four or more than the only functions that are approximable on the interval by polynomials with integer coefficients are these polynomials them
3、selves. (2) If is a continuous function on an interval I of length strictly less then 4,then is approximable on the interval by polynomials with integer coefficients if and only if its interpolating polynomial on has integer coefficients.Keywords: approximation; p
4、olynomial with integer coefficients; interpolating polynomial; algebraic integer.目 录中文摘要 1英文摘要 1前言21 1些符号与专用术语22 区间长度大于等于4时整系数多项式逼近问题2 3 区间 与 上的整系数多项式逼近问题 44 区间长度小于4时的整系数多项式逼近问题94.1代数整数及其相关概念 104.2插值多项式105 结束语156 参考文献 16 【包括:毕业论文、开题报告、任务书】【说明:论文中有些数学符号是编辑器编辑而成,网页上无法显示或者显示格式错误,给您带来不便请谅解。】