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MathGroup Archive 1996

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Re: RSolve question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5528] Re: [mg5524] RSolve question
  • From: "w.meeussen" <w.meeussen at solair4b.eunet.be>
  • Date: Thu, 19 Dec 1996 01:02:29 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

At 19:26 14-12-96 -0500, you wrote:
>To the List:
>
>I appreciate if you can give me some input into the following math
>questions that puzzle me quite a bit:
>
>1) Why am I getting the following error?  This example came from
>Wolfram Koepf's PowerSeries`.  You don't need this package here.
>
>In[2]:=
>RSolve[{
>k*(1 + k)*a[k] + (1 + k)*(2 + k)*a[2 + k] == 0,
>a[0]==0, a[1]==1}, a[k], k]
>
>DSolve::dnim:
>   Built-in procedures cannot solve this differential
>     equation.
>DSolve::dnim:
>   Built-in procedures cannot solve this differential
>     equation.
>Out[2]=
>RSolve[{k (1 + k) a[k] + (1 + k) (2 + k) a[2 + k] == 0,
>   a[0] == 0, a[1] == 1}, a[k], k]
>
>TX in advance
>
>Daitaro Hagihara
>
>

hi,

my Mma 2.2.3 gives me the same result.

On close inspection, two remarks for you (to disregard if too silly):
*************************
First :

RSolve[{
k*(1 + k)*a[k] + (1 + k)*(2 + k)*a[2 + k] == 0,
a[0]==0, a[1]==1}, a[k], k]

should be equivalent to 

RSolve[{
k*a[k] + (2 + k)*a[2 + k] == 0,
a[0]==0, a[1]==1}, a[k], k]

if k is not == -1, right? so why the factor (k+1) ?
********************************
Second,

the sequence can be written as:

a[m_]:=-(m-2) a[m-2] /m ; a[1]=1;a[0]=0
0
and tabulated as :

Table[a[i],{i,10}]//InputForm
{1, 0, -1/3, 0, 1/5, 0, -1/7, 0, 1/9, 0}

and the slightly different equation gives :

RSolve[{
b[m]==(m-2)/m b[m-2],
b[0]==0,b[1]==1,b[2]==0}, b[m], m]//InputForm

{{b[m] -> (-2*If[m == -1, 1, 0] -
        If[m == 0, 0, -m^(-1)])/2 + 
     If[m == 0, 0, -((-1)^m/m)]/2}}

Table[b[m]/.Flatten[%]/.m->i,{i,10}]//InputForm
{1, 0, 1/3, 0, 1/5, 0, 1/7, 0, 1/9, 0}

*******************************

So, I think you have a valid "proto-bug-report" here for TechSupport.


Wouter.
Dr. Wouter L. J. MEEUSSEN
w.meeussen at solair4b.eunet.be



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