Re: Recursive Rules

*To*: mathgroup at smc.vnet.net*Subject*: [mg31156] Re: [mg31147] Recursive Rules*From*: BobHanlon at aol.com*Date*: Sun, 14 Oct 2001 04:11:49 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

In a message dated 2001/10/13 3:17:53 AM, mcoleman at bondspace.com writes: >I know that a recurrent/recursive function can be written > >f[t_] := f[t] = a + b*f[t-1]. > >So that once an initial value is stipulated, e.g., f[0]=0, then the >function "remembers" past values and can correctly calculate f[] for >any t. > >I was wondering if it was possible to do the same thing with a Rule? > Use ReplaceRepeated (//.) fact[0] = 1; fact[5] //. fact[n_] -> n*fact[n-1] 120 f[1] = c; f[4] //. f[n_] -> a+b*f[n-1] a + b*(a + b*(a + b*c)) Bob Hanlon Chantilly, VA USA