Find the inverse laplace transform :

$\displaystyle F(s) = \sqrt{ s + \sqrt{1+s^2}}$

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- Jun 14th 2009, 11:56 PMsimplependulumInverse Laplace Transform
Find the inverse laplace transform :

$\displaystyle F(s) = \sqrt{ s + \sqrt{1+s^2}}$ - Jun 16th 2009, 05:49 AMThe Second Solution
- Jun 16th 2009, 10:50 AMshawsend
If you mean Bromwich style, then look at this one first:

$\displaystyle \mathop\oint\limits_{H} e^{st}\sqrt{1+s^2}\,ds$ where $\displaystyle H$ is the contour below. It doesn't matter if this one doesn't have an inverse transform. Just first figure out how the integrand varies across the (finite) red-blue and yellow-green branch-cuts and also the remaining parts of the contour. Then try and extend that work to $\displaystyle F(s)$ above. However, this may not be the best contour to use.