$
Re[epsilon(omega) \/ epsilon.alt_0] =& 1 + 2 / pi cal(P) integral_0^oo (omega' Im[
    epsilon(omega') \/ epsilon_0
  ]) / (omega'^2 - omega^2) dif omega' \
  Im[epsilon(omega) \/ epsilon.alt_0] =& sigma / (epsilon_0 omega) - (2 omega) / pi cal(P) integral_0^oo (omega' Re[
    epsilon(omega') \/ epsilon_0 - 1
  ]) / (omega'^2 - omega^2) dif omega'
$