多项式序列一致逼近连续函数的两个结论

Two conclusions about uniform convergence of continuous function with polynomial sequence

对用多项式序列一致逼近有界区间的连续函数进行了讨论并得到两个结果:1.这种逼近可以进行的充分必要条件为函数是一致连续的;2.多项式序列的阶数的极限为正无穷.

This paper discusses the uniform approximation of continuous function on bounded intervals with polynomial sequence and gets two conclusions in the following： （ 1 ） The approximation exists if and only if the function is uniform continuous; （2） The limit of order of polynomial sequence is positive infinity.