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Math Help - complex inversion formula of laplace transforms - branch point

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    complex inversion formula of laplace transforms - branch point

    this is a problem of using hte complex inversion formula to solve the inverse laplace transform of...

    \mathcal{L}^{-1}(e^{\frac{-sx}{\sqrt{s^2 +1}}})

    the solutions given to us say that the bromich contour used must have a branch point at s = -1 ... i have no idea why
    Last edited by mr fantastic; October 16th 2009 at 09:59 PM. Reason: Edited title
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    Quote Originally Posted by walleye View Post
    this is a problem of using hte complex inversion formula to solve the inverse laplace transform of...

    \mathcal{L}^{-1}(e^{\frac{-sx}{\sqrt{s^2 +1}}})

    the solutions given to us say that the bromich contour used must have a branch point at s = -1 ... i have no idea why
    The singularity of the function (s = -1) is a branch point. Read these:

    Mathematical methods in chemical ... - Google Books

    http://books.google.com.au/books?id=...age&q=&f=false
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