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Fourier Transform of Ratio of Hyperbolic sines

by orstats
Tags: fourier, hyperbolic, ratio, sines, transform
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May6-08, 05:39 AM
P: 14

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.
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