# 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:

$\displaystyle L_j \left({X}\right) := \prod_{\substack{0 \mathop \le i \mathop \le n \\ i \mathop \ne j}} \frac{X - x_i}{x_j - x_i} \in \R \left[{X}\right]$

## Source of Name

This entry was named for Joseph Louis Lagrange.