Efficient application of the Chiarella and Reichel series approximation   of the complex error function
  Using the theorem of residues Chiarella and Reichel derived a series that can be represented in terms of the complex error function (CEF). Here we show a simple derivation of this CEF series by Fourier expansion of the exponential function $\exp ({- {\tau ^2}/4})$. Such approach explains the existence of the lower bound for the input parameter $y = \operatorname{Im} [z]$ restricting the application of the CEF approximation. An algorithm resolving this problem for accelerated computation of the CEF with sustained high accuracy is proposed. 
S. M. Abrarov, B. M. Quine and R. K. Jagpal
math.GM