It's been a couple years since I studied calculus but I wondered if it was possible to calculate the double differential of a set of discrete data points, and if so, how do I go about doing this. What I mean is:
If I have a sequence of six data points: [1,2,3,4,5,6], can I process these in some way so that I find out what the second order differential is in the middle of this sequence (i.e. between 3 and 4). Obviously for this data it's 0 but I wondered if there was a standard method that could be applied to any sequence?
Something in my head says it's to do with the Taylor series or finite difference, but I am struggling to follow them and I might be way off.
Thanks so much.