Lagrange Interpolating Polynomials

A rearranged version of Newton’s Divided Difference Interpolating Polynomial.

$$L_{n,k}(x) = \prod_{i=0,i\neq k}^{n} \frac{x - x_i}{x_k - x_i}$$

$n$-th Lagrange interpolating polynomial is: $$

$$P_n(x)= \sum_{k=0}^n L_{n,k}(x)f(x_k)$$