The Fourier expansion approximation for high-accuracy computation of the Voigt/complex error function at small imaginary argument

TL;DR

This paper introduces a Fourier expansion-based approximation method to accurately and efficiently compute the Voigt/complex error function at very small imaginary arguments, addressing a known computational challenge.

Contribution

The paper presents a novel Fourier expansion approximation specifically designed for high-accuracy computation of the Voigt/complex error function at small imaginary parts.

Findings

Effective resolution of small imaginary argument computation issues

High-accuracy results demonstrated for challenging parameter ranges

Method improves computational speed and precision

Abstract

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 $y \to 0$.