Fourier Transform of Ratio of Hyperbolic sines

  1. Hello:

    I am referring to 'Table of Laplace Transforms' by Roberts&Kaufman. But I cannot seem to get a soln for the following Fourier Transform to retrieve my probability density f(x)

    c2 * Integral{e^(iwx) * sinh[sqrt(2w)c1] / sinh[sqrt(2w)pi] dw} = f(x)

    where -pi< c1 <=0 and c2 is a constant that scales the integral appropriately so that f(x) is p.d.f. Ratios such as these appear in heat transfer applications.
     
  2. jcsd
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