Re: Question
- To: mathgroup at smc.vnet.net
- Subject: [mg9411] Re: [mg9390] Question
- From: seanross at worldnet.att.net
- Date: Wed, 5 Nov 1997 01:56:29 -0500
- Sender: owner-wri-mathgroup at wolfram.com
Boguslaw Ptaszynski wrote:
>
> Hello Mathematica (v.3,0 for Windows) Users,
> I have a question that I hope someone has an answer for. I have the
> following recurrence relation:
>
> a[n+2]= 1/(b^2) ( b/2 a[n] + n (n-1)/4 a[n-2] )
>
> for the indices in the series n>=2.
> I want to use the formula to determine the values of a[n] for
> n=2,3,4,...12 and give these values in the table
>
> I have written :
>
> Clear [a,n,b]
> a[n_] := a[n]= 1/(b^2) ( b/2 a[n-2] + (n-2) (n-3)/4 a[n-4] ); a[0]=a0;
> a[1]=a1;
> TableForm[ Table[{n, a[n]}, {n,0,12}]]
>
> an I have got the following message:
>
> $RecursionLimit::"reclim": "Recursion depth of \!\(256\) exceeded."
> $RecursionLimit::"reclim": "Recursion depth of \!\(256\) exceeded."
> $RecursionLimit::"reclim": "Recursion depth of \!\(256\) exceeded."
> General::"stop":
> "Further output of \!\($RecursionLimit :: \"reclim\"\) will be
> suppressed \
> during this calculation."
>
> What does the message mean? I will be happy to get any information
> abaout this problem.
>
> Boguslaw Ptaszynski
a[n] requires that a[n-2] and a[n-4] be specified. Since you have only
declared initial values for a[0] and a[1], I can't think of a single n
for which a[n] would be defined.
a[0] requires a[-2] and a[-4].
a[1] requires a[-1] and a[-3].
a[2] requires a[0](have that) and a[-2]. a[3] requires a[1] and a[-1].
a[4] requires a[2] and a[0](have that)
all other values of n>4 will require one of the preceding a[n]'s to be
defined and none of them are. I think you need to specify four values
of a[n] to define your function, 2 a[n]'s for even values of n and 2
for the odd ones.