Lagrange Interpolation

The polynomial given in (1.1) where li(x) are defined by (1.3) is called the Lagrange interpolating polynomial and li(x) are called the Lagrange fundamental polynomials.We can write the Lagrange fundamental polynomials l_i(x) in a simple notation.

Denote                                                                 

which is the product of all factors. Differentiating w(x) with respect to x and substituting x = x_i

we get

since all other terms vanish. Therefore, we can also write l_i(x) as

....................1.4