My question is as shown above. I have churned through the first part, but I am stuck on showing the orthogonality of the Lagrange polynomials.
My first hope was to use the fact that the Lagrange polys form the interpolating poly, but I have $k+1$ points, so can only form a degree $k$ polynomial - I was hoping to form $H_{k+1}$.
The main issue that I have is not knowing how to use the fact that the $x_j$ are the (distinct) zeros of the Hermite polys. Firstly, some advise on how to use this fact would be appreciated, and then maybe some more if I still can't do it (=P!).
Thanks! :)
[Apologies if this is a duplicate - I can't find its duplicate if it is; if it is, then please let me know and I'll remove the question. (Don't just mark as duplicate as I'll lose reputation and I have looked for a duplicate, but can't find it.)]