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laplace transform

  • To: mathgroup at
  • Subject: [mg65076] laplace transform
  • From: Marlies.Goorden at
  • Date: Tue, 14 Mar 2006 05:59:53 -0500 (EST)
  • Sender: owner-wri-mathgroup at

I have a problem with the Laplace transform of mathematica. I 
want to know the laplace transform of sin(a*t).
When I type
mathematica gives me
\sqrt(a^2) sign(a)/(a^2+s^2)

On the other hand my mathematics books gives the answer

For complex a the answer is not the same. If I choose for 
a=0.3+0.5i and
the two formulas give me 
-0.096+0.65i and 0.51+0.41i respectively.

A numerical integration,
i.e. NIntegrate[Sin((0.3+0.5i)*t)*Exp[-t],{t,0,Infinity}]
gives me the same numerical value as the mathematics book 
Is the mathematica formula wrong?
Thank you for your help,
Marlies Goorden

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