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MathGroup Archive 2002

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Re: help: recursive functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32635] Re: [mg32616] help: recursive functions
  • From: BobHanlon at aol.com
  • Date: Fri, 1 Feb 2002 02:02:41 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 1/31/02 2:13:14 AM, Okke at NOSPAMtref.nl writes:

>I'm having some problems with a recursive function.
>Could somebody please help me by telling me how I
>should enter such a function?
>
>tia,
>
>This is what I've done so far:
>
>f[n_]:=Sin[Pi*n*(0.05+(0.0005*n))]
>y[n_]:=1.5*y[n-1]-0.85*y[n-2]+f[n]
>
>I'm trying to Plot[y[n],{n,0,320}] but that gives me
>an error: $RecursionLimit::reclim: Recursion depth of 256 exceeded.
>
>btw, is there an option to fill the area under the sine?
>

You need to define some stopping values for the recursion.  
I also recommend adding "memory" to the recursion to speed 
it up.  For example,

f[n_]:=Sin[Pi*n*(0.05+(0.0005*n))];

y[0] = y[1]=0;

y[n_Integer]:= y[n]=1.5*y[n-1]-0.85*y[n-2]+f[n];

data=Table[y[n],{n,0,320}];

ListPlot[data, PlotJoined->True, ImageSize->350];

Needs["Graphics`FilledPlot`"];

FilledListPlot[data, PlotJoined->True, Fills->RGBColor[1, 0, 0],
 
    ImageSize->350];


Bob Hanlon
Chantilly, VA  USA


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