A rapid and highly accurate approximation for the error function of complex argument

TL;DR

This paper introduces a fast and precise approximation method for the error function of complex arguments using Fourier expansion, enabling high-accuracy computations suitable for rapid algorithms.

Contribution

It presents a novel Fourier-based approximation of the complex error function that achieves high accuracy and computational efficiency.

Findings

Matches reference values up to the last decimal digit

Highly accurate approximation demonstrated

Suitable for rapid computational algorithms

Abstract

We present efficient approximation of the error function obtained by Fourier expansion of the exponential function $\exp [{- {(t - 2 \sigma)^2}/4}]$. The error analysis reveals that it is highly accurate and can generate numbers that match up to the last decimal digits with reference values. Due to simple representation the proposed error function approximation can be utilized in a rapid algorithm.