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:
 * $\ds \map {L_j} X := \prod_{\substack {0 \mathop \le i \mathop \le n \\ i \mathop \ne j} } \frac {X - x_i} {x_j - x_i} \in \R \sqbrk X$

Also see

 * Definition:Lagrange Interpolation Polynomial