Re: Better recursive method?

*To*: mathgroup at smc.vnet.net*Subject*: [mg72831] Re: Better recursive method?*From*: Johan Grönqvist <johan.gronqvist at gmail.com>*Date*: Sun, 21 Jan 2007 06:14:02 -0500 (EST)*References*: <eosh0f$9bs$1@smc.vnet.net>

nandan skrev: > This should be pretty easy to calculate for Mathematica. I have written > it the following way: > pi[0,theta] := 0; > pi[1,theta] := 1; I believe this should be pi[0,theta_] := 0 > pi[i_, theta_] := pi[i, theta] =(2n-1)/(n-1) Cos[theta] pi[i-1, theta] > - n/(n-1) pi[i-2,theta] Here n is a free variable, and I get a huge expression when trying to evaluate this. Is it correct to guess that n should be i? I also believe that in general it is best to add an N[...] in the definition of pi, to avoid a large polynomial expression in rational numbers and Cos[theta]. If that is the case, and after setting $RecursionLimit = Infinity, it takes me 0.052003 Second to calculate pi[1000,1]. My kernel quits silently when attempting pi[10000,1], and I would be interested in knowing why. > in IDL, it calculates > in fraction of a second. Even the simple calculation of 'pi[40,pi/4]' > took more than 350 seconds. > > What could be the problem in my logic. Is there any other better way to > write recursive functions in Mathematica? > I believe it is about avoiding analytical expressions when you only want numerical answers. Hope this can help somewhat. / johan