How to decompose a function into exponential functions?

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SUMMARY

The discussion focuses on decomposing a complex function defined on positive integers (Z+) into a sum of exponential functions of the form A_i exp(k_i x). It is established that with six exponential functions, one can determine 12 constants (A_i and k_i) to fit the function through any 12 points. If the original function requires fitting through more than 12 points, additional exponential functions will be necessary to achieve an accurate decomposition.

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wdlang
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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?
 
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If you have 6 functions of the form [itex]A_ie^{k_ix}[/itex] 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.
 

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