Does a 'general extrapolation formula' exist?...

Ladies and Gentleman…

… at the end of this thread…

http://www.mathhelpforum.com/math-he...variables.html

… Opalg kindly invited me to ask you some questions regarding a problem about which I’m working now. The problem is to examine the possibility to full reconstruction of a function from the knowledge of a discrete set of value . I started supposing that is a complex variable function which is analytic in the whole complex plane, i.e. that is an *entire function*, so that we can write it as Taylor expansion around …

(1)

We consider ‘sampled’ on the real axis at with , call the ‘samples’ and use them to construct the following real variable function…

(2)

In order to find the let’s write (2) ‘in extenso’…

(3)

Comparing (2) and (3) it is easy to observe that the obey to the recursion formula…

(4)

At this point some question for you…

a) what I have done till now is correct or not?…

b) what can we say more about the and the ?…

Kind regards