Definition:Lagrange Basis Polynomial

Definition
Let $x_0,\ldots,x_n \in \R$ be real numbers.

The Lagrange basis polynomials associated to the $x_i$ are the polynomials:
 * $\displaystyle L_j(X) = \prod_{\substack{0 \leq i \leq n\\i \neq j}} \frac{X - x_i}{x_j - x_i} \in \R[X]$