Inverse Laplace transform of a function having algebraic singularity
Submitted by Structure on Sat, 12/22/2007 - 22:59.
Laplace inverse transform of
This function has two singular points, zero and none of them isolated.
We use the differential equation satisfied by F:
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Let
Then
So
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Or
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Or
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Or
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or
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Now
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and
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But is equivalent at
to
and then their Laplace transform are equivalent at s=0 But
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From
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we have
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.
Finally we have
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