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

S. M. Abrarov; B. M. Quine; R. K. Jagpal

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arXiv · 1208.2062

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

S. M. Abrarov·B. M. Quine·R. K. Jagpal

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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 $\exp ({- {\tau ^2}/4})$. 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.

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BibTeX RIS

S. M. Abrarov, B. M. Quine, R. K. Jagpal. 2012-08-10. Efficient application of the Chiarella and Reichel series approximation of the complex error function. https://arxiv.org/abs/1208.2062

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