可微函数的Taylor平均

On the Approximation of Differentiable Functions by Taylor Means

给出了ｆ（ｘ）∈Ｃｒ２π的Ｔａｙｌｏｒ平均Ｔｎ，α（ｆ，ｘ）与ｆ（ｘ）差的主项展开式和ｓｕｐｆ∈ωｒＨωｍａｘｘ｜Ｔｎ。

Let f∈C r 2π , denote by T n,α (f,x) the n th Taylor means of  f(x). The asymptotic representations of the deviation T n,α (f,x)-f(x) and the quantity  sup f∈ω rH ω max x|T n,α (f,x)-f(x)| were given in this paper.