MathGroup Archive 1997

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg9414] Re: Question
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Wed, 5 Nov 1997 01:56:31 -0500
  • Organization: University of Western Australia
  • Sender: owner-wri-mathgroup at wolfram.com

Boguslaw Ptaszynski wrote:

>         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;

Your recurence links a[n] to a[n-4].  Hence you need to supply FOUR
initial values.  This is what led to the $RecursionLimit error
messages.  Assuming that a[n]=0 for n<0, i.e.

  In[1]:= a[n_] := a[n] = Simplify[(1/4*(n - 3)*(n - 2)*a[n - 4] + 
        1/2*b*a[n - 2])/b^2]; 
  
  In[2]:= a[0] = a0; a[1] = a1; a[n_ /; n < 0] = 0;

  In[3]:= Table[a[n], {n, 0, 12}]
  Out[3]=
	         a0   a1   3 a0  7 a1  15 a0  27 a1  105 a0
	{a0, a1, ---, ---, ----, ----, -----, -----, ------, 
	         2 b  2 b     2     2     3      3       4
	                   4 b   4 b   8 b    8 b    16 b
 
  321 a1  945 a0  2265 a1  10395 a0
  ------, ------, -------, --------}
      4       5        5        6
  16 b    32 b     32 b     64 b

Cheers,
	Paul 

____________________________________________________________________ 
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907       
mailto:paul at physics.uwa.edu.au  AUSTRALIA                            
http://www.pd.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________


  • Prev by Date: Problem with Integrate
  • Next by Date: Re: Programming page break
  • Previous by thread: Re: Question
  • Next by thread: Re: Question