I never could imagine that this problem was not already considered by mathematicians. Indeed I found a first reference that there is a whole theory about the topic by Norlund. Look here into some free pages of the book
The Calculus of Finite Differences by Louis Melville Milne-Thomson (2000).
EDIT: Actually I see that the book was already published in 1933. You can download a copy here.
The Calculus of Finite Differences by Louis Melville Milne-Thomson (2000).
EDIT: Actually I see that the book was already published in 1933. You can download a copy here.
