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of a function <math>f\in C[a,b]</math> is the function <math>\omega_n:[0,\infty)\to\mathbb{R}</math> defined by
:<math>\omega_n(t,f,[a,b])=\sup_{h\in[0,t]}\sup_{x\in[a,b-nh]}|\Delta_h^n(f,x)|</math> for <math>t\in\left[0,\frac{b-a}{n}\right],</math>
and
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