# Math Help - [SOLVED] Hermite Interpolating Polynomial

1. ## [SOLVED] Hermite Interpolating Polynomial

I saw a previous thread that was related, but it seemed to be missing some information, and it was never solved.

I know that for Hermite interpolation, every textbook has
$
K_{2n+1}(x) = \sum_{j=0}^n f(x_j) H_{n,j}(x) + \sum_{j=0}^n f'(x_j) \hat H_{n,j}(x)
$

where

$
H_{n,j}(x) = [1 - 2(x-x_j)L'_{n,j}(x_j)]L^2_{n,j}(x)
$

and

$
\hat H_{n,j}(x) = (x-x_j)L^2_{n,j}(x)
$

But how do I make it to the next step? What's the 3rd term, if I'm looking for $\tilde H_{n,j}(x)$ such that
$
\tilde H''_{n,j}(x_i) = \begin{cases}
1 &\text{ if } i=j\\
0 &\text{ otherwise}
\end{cases}
$

I would love to know if you could offer any help. I'm stumped...

2. Well, found my answer here.

I'll get back to you with any more questions plaguing me.