I'm trying to brush the dust of my transform tinkering. (Have to use it in some electronic stuff.) I just did an exercise where I calculate the F-transform of an even function.
Let f(x) be:
Find the even Fourier transform.
I calculated the transform with this formula
Knowing that the function is even I write:
A bit integration gives, don't hesitate to call out errors.
Now as an application to this calculation I'm supposed to determine this integral.
This is where I like to get some help... I simply don't know how to do it. Calculating the integral, in an other way, I get