On a remarkable formula of Ramanujan
  A simple proof of Ramanujan's formula for the Fourier transform of the square of the modulus of the Gamma function restricted to a vertical line in the right half-plane is given.   The result is extended to vertical lines in the left half-plane by solving an inhomogeneous ODE. We then use it to calculate the jump across the imaginary axis. 
Debraj Chakrabarti and Gopala Krishna Srinivasan
math.CA math.CV