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Bug in LaplaceTransform?

• To: mathgroup at smc.vnet.net
• Subject: [mg97693] Bug in LaplaceTransform?
• From: Wieland Brendel <wielandbrendel at gmx.net>
• Date: Thu, 19 Mar 2009 02:09:00 -0500 (EST)

Dear reader,
how can it happen that Mathematica throws out -i for the Laplace 
transform of one,

LaplaceTransform[1, t, I] = -i?

After all the Laplace transformation (with s = I) is defined as

Integrate[Exp[-I t], {t, 0, Infinity}]

and should be undefined. Am I wrong or is this a bug?

Thanks for an answer!
Wieland

• Follow-Ups:
  • Re: Bug in LaplaceTransform?
    • From: Daniel Lichtblau <danl@wolfram.com>