The Fourier expansion approximation for high-accuracy computation of the   Voigt/complex error function at small imaginary argument
  It is known that the computation of the Voigt/complex error function is problematic for highly accurate and rapid computation at small imaginary argument $y << 1$, where $y = \operatorname{Im} \left[ z \right]$. In this paper we consider an approximation based on the Fourier expansion that can be used to resolve effectively such a problem when $y \to 0$. 
S. M. Abrarov and B. M. Quine
math.NA