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Topic: Rubi 4.5 released
Replies: 21   Last Post: Jun 29, 2014 4:29 AM

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Nasser Abbasi

Posts: 5,690
Registered: 2/7/05
Re: Rubi 4.5 released
Posted: Jun 24, 2014 6:35 AM
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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




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