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:

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

This article, or a section of it, needs explaining. In particular: $\R \sqbrk X$ You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Explain}} from the code.

There is believed to be a mistake here, possibly a typo. In particular: Not sure if it's a mistake or a different way of defining it, but 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics: Lagrange interpolation formula has this wrapped up in another product symbol You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by reviewing it, and either correcting it or adding some explanatory material as to why you believe it is actually correct after all. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Mistake}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Source of Name

This entry was named for Joseph Louis Lagrange.

Also see

• Definition:Lagrange Interpolation Polynomial