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