laplace transform



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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