
Re: Rubi 4.5 released
Posted:
Jun 24, 2014 6:35 AM


On 6/24/2014 1:52 AM, clicliclic@freenet.de wrote:
..... > Now c should > be replaced by COS(p) and this result be integrated from p=0 to p=2*pi; > for symmetry reasons it suffices to integrate from p=0 to p=pi and to > double the result, whereby the singularity of SQRT(c^2  1) at c^2 = 1 > is avoided. > > Martin. >
The outer integral keeps giving me a recursion error.
Got passed the inner one, and taking the limits from r=0..infinity, but when integrating this for `p`, a problem shows up. Here is the code, may be someone can try it. Version 9.01, Rubi 4.5:
 Clear[r, z, a, c, p]; (*this below copied from Martin's post as is*)
integrand1 = 192*r*z^2*(a^2  4*c^2*r^2)*(16*z^4*(a^2 + 4*r^2) + (8*z^2 + a^2 + 4*r^2)*(a^4 + 8*a^2*r^2*(1  2*c^2) + 16*r^4))/ ((a^4 + 8*a^2*r^2*(1  2*c^2) + 16*r^4)*((4*z^2 + a^2)^2 + 8*r^2*(4*z^2 + a^2*(1  2*c^2)) + 16*r^4)^(5/2));
integrand2 = 48*r*z*(4*c^2*r^2  a^2)/((a^2  4*a*c*r + 4*r^2)*(4*z^2 + a^2 + 4*a*c*r + 4*r^2)^(5/2));
integrand3 = 48*r*z*(4*c^2*r^2  a^2)/((a^2 + 4*a*c*r + 4*r^2)* (4*z^2 + a^2  4*a*c*r + 4*r^2)^(5/2));
(* now find the inner integral, use the assumptions *)
res = Assuming[Element[{r, p, a, z}, Reals] && {z > 0, 1 < c < 1}, Int[integrand1, r] + Int[integrand2, r] + Int[integrand3, r]];
(*ok, successes now find the limits to do the outer integral *) low = Limit[res, r > 0]; up = Limit[res, r > Infinity]; integrand4 = up  low;
(*replace c by Cos[p] *) integrand5 = integrand4 /. c > Cos[p]
(* do the outer integral *) res2 = Assuming[Element[{r, p, a, z}, Reals] && z > 0, Int[integrand5, p]];
(*after one hr or so ...*)
$RecursionLimit::reclim: Recursion depth of 1024 exceeded. >> $RecursionLimit::reclim: Recursion depth of 1024 exceeded. >>
I tried the last integration also with Mathematica Integrate, but stopped it after 2 hrs to use the computer. Was still busy. Will try it again later, but does not look good *)
Nasser

