wip

插值

差分

$$ f[x_0,\cdots,x_{k+1}] = \frac{f[x_0,\cdots,x_k]-f[x_1,\cdots,x_{k+1}]}{x_0-x_{k+1}} $$

$$ f[x_0,\cdots,x_{k}] = \frac{f^{(k)}(\xi)}{k!} \qquad \xi \in (x_{min},x_{max}) $$

$$ \begin{aligned} f(x) &= f(x_0) + fx_0,x_1 + fx_0,x_1,x_2(x-x_1) + \cdots \newline &+ fx_0,\cdots,x_n\cdots(x-x_{n-1}) \newline &+ fx,x_0,\cdots,x_n\cdots(x-x_{n-1})(x-x_n) \end{aligned} $$

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