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Using the theorem of residues Chiarella and Reichel derived a series that canbe represented in terms of the complex error function (CEF). Here we show asimple derivation of this CEF series by Fourier expansion of the exponentialfunction $\exp ({- {\tau ^2}/4})$. Such approach explains the existence of thelower bound for the input parameter $y = \operatorname{Im} [z]$ restricting theapplication of the CEF approximation. An algorithm resolving this problem foraccelerated computation of the CEF with sustained high accuracy is proposed.

Efficient application of the Chiarella and Reichel series approximation of the complex error function