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<math>\Delta_h^n(f,x_0)=\sum_{i=1}^n(-1)^{n-i}\binom{n}{i} f(x_0+ih).</math>
===Properties
1. <math>\omega_n(0)=0,</math> <math>\omega_n(0+)=0.</math>
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6. For <math>r\in N</math>, denote by <math>W^r</math> the space of continuous function on <math>[-1,1]</math> that have <math>(r-1)</math>-st absolutely continuous derivative on <math>[-1,1]</math> and <math>\|f^{(r)}\|_{L_{\infty}[-1,1]}<+\infty.</math> If <math>f\in W^r</math>, then <math>\omega_r(t,f,[-1,1])\leq t^r\|f^{(r)}\|_{L_{\infty}[-1,1]}, t\geq 0.</math>
Here <math>\|g(x)\|_{L_{\infty}[-1,1]}=\sup_{x\in [-1,1]}|g(x)|.</math>
===Application===
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