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