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Re: finding explicit rule for series

• To: mathgroup at smc.vnet.net
• Subject: [mg52068] Re: finding explicit rule for series
• From: David Bailey <dave at Remove_Thisdbailey.co.uk>
• Date: Tue, 9 Nov 2004 01:37:16 -0500 (EST)
• References: <cmnaup$7vv$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

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