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inverse laplace transform

• To: mathgroup at smc.vnet.net
• Subject: [mg77601] inverse laplace transform
• From: dimitris <dimmechan at yahoo.com>
• Date: Wed, 13 Jun 2007 07:45:20 -0400 (EDT)

Is anybody familiar with on line notebooks regarding
inversion of laplace transforms via Bromwich integral
formula, within Mathematica?

For example, the function Cosh[x*Sqrt[s]]/(s*Cosh[Sqrt[s]])
has infinitely many singularities (note that s=0 is not a branch point
as a quick look might indicate).
It can be deduced that the function has poles at s=0 and s=s[n]
where s[n]=-(n^2-1/2)^2 Pi^2, n=1,2,3,...
I can perform its inversion by hand, (Mathematica
InverseLaplaceTransform
at least in vrsion 5.2 fails for this task) but I wonder if somebody
has worked
with such Bomwich integrals within Mathematica or the well known
modification
of Bromwich contour in case of branch points.

BTW, what does version 6 do?

Dimitris