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

2012/08/10 by Abrarov, S. M., Quine, B. M., Jagpal, R. K.
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.1208.2062

Abstract

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 (- τ²/4). Such approach explains the existence of the lower bound for the input parameter y = 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.

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