Well, found my answer here.
I'll get back to you with any more questions plaguing me.
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
where
and
But how do I make it to the next step? What's the 3rd term, if I'm looking for such that
I would love to know if you could offer any help. I'm stumped...