A rearranged version of Newton’s Divided Difference Interpolating Polynomial. Ln,k(x)=∏i=0,i≠knx−xixk−xiL_{n,k}(x) = \prod_{i=0,i\neq k}^{n} \frac{x - x_i}{x_k - x_i} Ln,k(x)=i=0,i=k∏nxk−xix−xi nnn-th Lagrange interpolating polynomial is: Pn(x)=∑k=0nLn,k(x)f(xk)P_n(x)= \sum_{k=0}^n L_{n,k}(x)f(x_k) Pn(x)=k=0∑nLn,k(x)f(xk)