Re: Differences between recursions and limit

*To*: mathgroup at smc.vnet.net*Subject*: [mg60551] Re: Differences between recursions and limit*From*: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>*Date*: Tue, 20 Sep 2005 05:19:06 -0400 (EDT)*Organization*: Uni Leipzig*References*: <dgm01k$njm$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, look in the manual about dynamic programming and change your definition to x[0]=0; x[k_] :=x[k]= .25 *(1 + x[k-1] + (x[k-1])^2 + (x[k-1])^3); Regards Jens "anbra1" <xyxanbra1 at tiscalixxxyxxx.it> schrieb im Newsbeitrag news:dgm01k$njm$1 at smc.vnet.net... | Please, | I want to know | why these two recursions,doing the same thing, | are the first one much more slow than the second | | ------------------------- | | x[0]=0; | x[k_] := .25 *(1 + x[k-1] + (x[k-1])^2 + (x[k-1])^3); | | For[k=1,k<12,Print[k," ",SetPrecision[x[k],30]];k++] | | ------------------------- | | a=0; | | For[k=1,k<12,k++, | | b= .25 (1 + a + a^2 + a^3);a:=b;Print[k," ",SetPrecision[b,30]]] | | ------------------------- | Another question | How can I calculate | the limit of this recursion for k->Infinite ? | Thank you all | |