I too was impressed by what Mathematica could do and looked into getting it. I gave up when I learned they will not sell the student version to a retired electrical engineer pursuing math studies as a hobby. Next year I could get the professional version with a senior discount, but even 50% off is too steep for me.
When I said Mathematica handles it, this is what I meant: In the paper where I found the expression for r(n,p), the authors gave a table of results for a small number of nodes. For example, r(0,1)=0.5; r(1,1)=2/pi; r(1,3)=-4+46/3pi (the one I tried); r(2,5)=(97/2)-(2236/15pi); etc. (I know the first two are correct.) The authors said these results were gotten from Mathematica, and gave the commands, which were essentially the two function definitions I used, but in Mathematica form. In the second function the entire expression I used was given as an argument to the Simplify command. I don't know if it corresponds to the Maxima simplify command, but it probably wouldn't help if the integration is bombing out. I guess I'll go try it anyway.
Bob Baker
> Date: Thu, 13 Mar 2008 10:45:39 -0700> From: dlakelan at street-artists.org> To: b_baker at hotmail.com> Subject: Re: [Maxima] New Maxima user has problem
> I'm impressed that Mathematica handles this integral. I'm even more > impressed that its result is in agreement with the result of maxima's > numerical procedures... I've heard that Mathematica sometimes > confidently throws back incorrect answers, though that was more from mid > 1990's versions.