# the inverse laplace transform of an exponential function

I was solving differential equations by using laplace transform, but I am stuck here trying to find the laplace inverse below, can anyone help? $$\mathcal L^{-1} \Biggl[ \sum_{m=0}^\infty \sum_{n=0}^\infty (2iK^2)^n \left(\exp\left(-(1+2m-z') \sqrt{\frac{s-B}{A}}\right) -\exp\left(-(1+2m+z')\sqrt{\frac{s-B}{A}}\right)\right) \cdot s^{-(n+1)}\Biggr]$$ where $A$ and $B$ are parameters. Any suggestions? Thank you.

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I tried to texify your input but there were some non-readable characters in it, please check if I've done correctly and remove the original input then ... –  martini Oct 1 '12 at 10:03
thank you. that's correct. –  sani Oct 1 '12 at 10:57