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What is $\prod_{n+1}(x)$ in the inequality $$|R_n(x)|\le \frac{M_{n+1}}{(n+1)!}|\prod_{n+1}(x)|?$$

$M_{n+1}$ is defined as $M_{n+1}=\max_{t\in[a,b]}|f^{n+1}(t)|$ where $a=\min\{x,x_0\},b=\max\{x,x_n\}$. What is the definition of $\prod_{n+1}(x)$?

user156262
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  • It is a product: (x - x_0)(x - x_1)...(x - x_n) where x_1, x_2, ..., x_n are nodes.

    I hope you can get this if you try to derive this result. Approximating a function with nth degree polynomial when (n+1) nodes are given. This, R_n(x) is often called the Error in Interpolating Polynomial.

     – Aniruddha Deshmukh Jul 06 '17 at 10:57
  • Where have you encountered this inequality? – Wojowu Jul 06 '17 at 11:02

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