How can I correctly perform Fourier inversion of function S(q) to get G(r)?

[enrikofermi]

Hi all.
I have to do Fourer inversion of an equation 7.46 but I don't know how to do that.
If anybody has any idea it wolud be very helpfull.
Inversion of S(q) is G(r).

 

[Dr. Courtney]

Is this homework help?

 

[enrikofermi]

No. I'm learning some physics and need to calculate this to get next step, but i can't. :/

 

[Dr. Courtney]

Did you try Wolfram Alpha?

I can't see the whole problem, plus it is sideways.

 

[enrikofermi]

No, didn't. That is whole problem, to do Fourier inverse of 7.46. Sorry because it is sideways. :/

 

[enrikofermi]

I have used Wolfram Alpha and got (almost) same result as I calculated earlier. (See pic) But in my book I have r instead of k in denominator. And that result in the book is fundamental! It must be correct. Where have Wolfram and me failed?