The Levi-Civita spacetime as a limiting case of the Gamma spacetime
  It is shown that the Levi-Civita metric can be obtained from a family of the Weyl metric, the Gamma metric, by taking the limit when the length of its Newtonian image source tends to infinity. In this process a relationship appears between two fundamental parameters of both metrics. 
L. Herrera, Filipe M. Paiva and N. O. Santos