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