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Math Help - Inverse Laplace Transform

  1. #1
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    Inverse Laplace Transform

    Find the inverse laplace transform :

     F(s) = \sqrt{ s + \sqrt{1+s^2}}
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  2. #2
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    Quote Originally Posted by simplependulum View Post
    Find the inverse laplace transform :

     F(s) = \sqrt{ s + \sqrt{1+s^2}}
    Has this arisen from a problem you're working on or have you been asked point blank to find it?
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  3. #3
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    Quote Originally Posted by simplependulum View Post
    Find the inverse laplace transform :

     F(s) = \sqrt{ s + \sqrt{1+s^2}}
    If you mean Bromwich style, then look at this one first:

    \mathop\oint\limits_{H} e^{st}\sqrt{1+s^2}\,ds where 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 F(s) above. However, this may not be the best contour to use.
    Attached Thumbnails Attached Thumbnails Inverse Laplace Transform-h-contour.jpg  
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