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Marie_Curie

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## Homework Statement

Hi there!

I'm just trying to figure out the Fourier transform of the hyperbolic secant function... I already know the outcome:

4[itex]\sum\ ((-1)^n*(1+2n))/(ω^2*(2n+1)^2) [/itex]

But sadly, I cannot figure out how to work round to it! :( maybe one of you could help me...

## Homework Equations

I was thinking of using the geometric series 1/(1+q) = [itex]\sum (-q)^n [/itex] for q = e^(-2*x), as the hyperbolic secant is 2*e^(-x)/(1+e^(-2*x)) .

And then you need to multiply the hyperbolic secant with e^(iωt) and integrate from -∞

up to ∞.

But... frankly, that was it. I have never managed to come to the result

4[itex]\sum\ ((-1)^n*(1+2n))/(ω^2*(2n+1)^2) [/itex]

Maybe someone could give me a hint to to solve this problem...? :)

Lots of greetings,

Marie

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