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
2/ when laplace is unable to compute the answer, it could (should ?) call
specint
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 ?
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
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