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vytrvalost Sep18-08 12:48 AM

Fourier transform (FT) of a Hyperbolic secant

Did anyone know how to do the Fourier transform of the hyperbolic
secant? I know the answer; it's given in the text (I'm reading
Ablowitz, Fokas, Complex Variables), it's another hyperbolic secant,
but I want to know how to do it. My dilemma is:

a) what contour to use? I'm having difficulty showing that the
contour integration goes to zero on the semicircle as the radius R
goes to infinity, particularly in the theta, angle, dependence in the
bottom, denominator, for e^z + e^{-z}

b) There are an infinite number of singularities along the imaginary
axis. Do I sum them up?

Thank you for your time my friend, I wanted to throw this out there. -vy
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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