> 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.
>>
>> 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?
No, but they have same derivative and same numerical value at s=-6*%i (I
was unable to compute numerical values at other simpler points)
(%i106) d:specint(sin(2*t)/t*exp(-s*t),t)-atan(2/s);
(%o106) %i*log((s-2*%i)/(s+2*%i))/2-atan(2/s)
(%i107) radcan(diff(d,s));
(%o107) 0
(%i108) subst(s=-6*%i,d),numer;
(%o108) 2.2204460492503131E-16*%i
Eric
>
> Ray
>
>>
>> What I can do is only this :
>> (%i56) u:specint(sin(2*t)/t*exp(-s*t),t);
>> (%o56) %i*log((s-2*%i)/(s+2*%i))/2
>> (%i57) trigrat(u);
>> (%o57) atan2(4*s/(s^2+4),(s^2-4)/(s^2+4))/2
>> which is obviously real for real s, but still quite complicated.
>>
>> Eric
>>
>>> Try specint, which handles Laplace transforms better:
>>>
>>> Specint(sin(2*t)/t*exp(-s*t),t) ->
>>>
>>> %i*log((s-2*%i)/(s+2*%i))/2
>>>
>>> (Don't know if that's right or not.)
>>>
>>> Ray
>>>
>>>
>>> -----Original Message-----
>>> From: maxima-bounces at math.utexas.edu
>>> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of
>>> eric.reyssat at math.unicaen.fr
>>> Sent: Thursday, February 26, 2009 9:15 AM
>>> To: maxima at math.utexas.edu
>>> Subject: laplace transform
>>>
>>> Hello,
>>>
>>> how comes that maxima pretends the following Laplace integral is
>>> divergent ?
>>> The function to integrate is not defined at 0, but the integral
>>> converges for every positive s.
>>> "integrate" doesn't find the answer.
>>> The value of the integral should be atan(2/s), as checked for s=3 by
>>> numerical computation with quad_qag :
>>>
>>> (%i1) build_info()$
>>> Maxima version: 5.17.0
>>> Maxima build date: 19:8 12/4/2008
>>> host type: i686-pc-mingw32
>>> lisp-implementation-type: GNU Common Lisp (GCL)
>>> lisp-implementation-version: GCL 2.6.8
>>>
>>> (%i2) display2d:false$ assume(s>0)$ laplace(sin(2*t)/t, t, s);
>>> Integral is divergent
>>> -- an error. To debug this try debugmode(true);
>>> (%i5) integrate(sin(2*t)/t*exp(-s*t),t,0,inf);
>>> (%o5) 'integrate(%e^-(s*t)*sin(2*t)/t,t,0,inf)
>>> (%i6) s:3$ quad_qag(sin(2*t)/t*exp(-s*t),t,.000001,1000,1);
>>> [atan(2/s)],numer;
>>> (%o7) [0.58800060355057,2.2822993845756943E-10,285,0]
>>> (%o8) [0.58800260354757]
>>>
>>>
>>> Eric Reyssat
>>> _______________________________________________
>>> Maxima mailing list
>>> Maxima at math.utexas.edu
>>> http://www.math.utexas.edu/mailman/listinfo/maxima
>>>
>>
>
>
>