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Re: finding explicit rule for series


Uwe Ziegenhagen wrote:
> Hello,
> 
> i have a series of numbers and would like to use Mathematica to find the 
> explicit algorithm in that way:
> 
> n(i)=5342543+n(i-1)....
> 
> I already spent some time with the manual, but didn't find anything.
> 
> Uwe
> 

If your series of numbers is finite (otherwise you would have a formula 
for n[i]) then you are, in effect, trying to fit an arbitrary function 
to a fixed set of points. There will be an infinite number of possible 
solutions to that problem. Maybe I am not understanding your question.

However, you could produce a list of possible solutions with unknown 
parameters (alpha and beta in this case) - e.g. n[i]:=alpha*n[i-1]+beta 
- which would give you a set of simultaneous equations for the 
parameters. If you can fit more than one 'model' then you obviously need 
more points of your sequence.

David Bailey


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