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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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