{P}_{n}\left(x \right)={c}_{0}+{c}_{1}\left(x-{x}_{0} \right)+{c}_{2}\left(x-{x}_{0} \right)\left(x-{x}_{1} \right)+...+{c}_{n}\left(x-{x}_{0} \right)\left(x-{x}_{1} \right)...\left(x-{x}_{n-1} \right).