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laplace transform

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

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

On the other hand my mathematics books gives the answer
a/(s^2+a^2)

For complex a the answer is not the same. If I choose for
example
a=0.3+0.5i and
s=1
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
formula.
Is the mathematica formula wrong?