# Notes: An assessment of some closed-form expressions for the Voigt function III: Combinations of the Lorentz and Gauss functions

## TL;DR

This paper reviews various pseudo-Voigt functions, which are linear combinations of Lorentz and Gauss functions, assessing their accuracy as approximations for the Voigt function through comparison with reference values.

## Contribution

It provides a comprehensive review and comparison of multiple closed-form pseudo-Voigt approximations for the Voigt function, highlighting their accuracy limitations.

## Key findings

- Relative errors can reach several percent
- Some approximations show significant deviations from reference values
- The review clarifies the accuracy trade-offs of different formulas

## Abstract

A variety of "pseudo-Voigt" functions, i.e. a linear combination of the Lorentz and Gauss function (occasionally augmented with a correction term), have been proposed as a closed-form approximation for the convolution of the Lorentz and Gauss function known as the Voigt function. First, a compact review of several approximations using a consistent notation is presented. The comparison with accurate reference values indicates relative errors as large as some percent.