p(x)=anxn+an−1xn−1+⋯+a2x2+a1x+a0,p(x) = a_nx^n + a_{n-1}x^{n-1} + \dots + a_2x^2 + a_1x + a_0, \\p(x)=anxn+an−1xn−1+⋯+a2x2+a1x+a0,
where p(xi)=yi for all i∈{0,1,…,n}p(x_i) = y_i \text{ for all } i \in \{ 0,1,\dots,n \}p(xi)=yi for all i∈{0,1,…,n}.
Lagrange polynomial: p(x)=∑i=0n(∏0≤j≤n;j≠ix−xjxi−xj)yip(x) = \sum_{i=0}^n ( \prod_{0 \leq j \leq n; j \not= i} \frac{x-x_j}{x_i-x_j} ) y_ip(x)=∑i=0n(∏0≤j≤n;j=ixi−xjx−xj)yi
More detailed info: https://en.wikipedia.org/wiki/Polynomial_interpolation
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