How to decompose a function into exponential functions?

[wdlang]

now i have a function defined on Z+

that is, it is defined on all positive integers, and it is complex

now i know that it is the sum of a few (perhaps 6) exponential functions in the form of A_i exp(k_i x)

how can i decompose the original function into the exponential functions? i.e., determine the values of k_i and A_i?

 

[HallsofIvy]

If you have 6 functions of the form A_ie^{k_ix} then you have 12 constants you can set. That means that you can set your functions to pass through any 12 points. If you have more than that, you will need more functions.