On Thu, Feb 26, 2009 at 6:13 PM, Raymond Toy <raymond.toy at stericsson.com> wrote:
> eric.reyssat at math.unicaen.fr wrote:
>> Yes, the answer given by specint (all in lowercase) is true, thank you.
>>
>> But
>>
>> 1/ I still don't understand the error message given by laplace
>
> Sounds like a bug in laplace
>>
>> 2/ when laplace is unable to compute the answer, it could (should ?) call
>> specint
>
> I think this has been discussed before. ?But AFAIK, no one has actually
> done anything about it.
Laplace calls defint with wrong arguments:
(%i4) trace(defint)$
(%i5) laplace(sin(2*t)/t,t,s);
1 Enter defint[2/(s10^2+4),s11,s,inf]
Integral is divergent
-- an error. To debug this try debugmode(true);
I guess s11 should be s10.
>>
>> 3/ Since I assumed s>0, I expected the answer to be given in a real form,
>> I mean without %i in it. How can we "simplify" this answer to atan(2/s) ?
>> Is there a quite general way to do it ?
>
> I don't know how to get anything simpler than
> atan2(4*s/(s^2+4),(s^2-4)/(s^2+4))/2. ?It seems to me that we could at
> least have atan2(4*s,s^2-4)/2, but I don't know how to get maxima to do
> that. ?I also don't know why you think the answer is atan(2/s). ?Is that
> the answer in some table of transforms?
(%i1) assume(s>0);
(%o1) [s>0]
(%i2) u:specint(sin(2*t)/t*exp(-s*t),t);
(%o2) (%i*log((s-2*%i)/(s+2*%i)))/2
(%i3) rectform(u), logexpand=all;
(%o3) atan(2/s)
--
Andrej