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- - **Fourier transform (FT) of a Hyperbolic secant**
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Fourier transform (FT) of a Hyperbolic secantHi,
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 data2. Relevant equations3. The attempt at a solution |

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