Power series for the half width of the Voigt function, rederived
DOI:
https://doi.org/10.33993/jnaat542-1640Keywords:
Voigt function, Faddeeva function, Maclaurin series, asymptotic series, high-precision computationAbstract
The Voigt function is the convolution of a Gaussian and a Lorentzian. We rederive power series for its half width at half maximum for the limiting cases of near-Gaussian and near-Lorentzian line shapes. We thereby provide independent verification and slight corrections of the expansion coefficients reported by Wang et al (2022). Results are used in our implementation of function voigt_hwhm in the open-source library libcerf.
Downloads
References
1] Voigt W (1912) Über das Gesetz der Intensitätsverteilung innerhalb der Linien eines Gasspektrums. Sitzungsber. Bayer. Akad. Wiss. Math.-Naturwiss. Kl. 25 603.
[2] NIST Digital Library of Mathematical Functions, http://dlmf.nist.gov.
[3] Johnson S G and Wuttke J (2013–2025) libcerf, a numeric library providing complex error functions. https://jugit.fz-juelich.de/mlz/libcerf (2013–2025).
[4] Wuttke J and Kleinsorge A Algorithm 1xxx: Code generation for piecewise Chebyshev approximation. submitted to ACM TOMS.
[5] Wang Y, Zhou B, Zhao R, Wang B, Liu Q and Dai M (2022) Super-Accuracy Calculation for the Half Width of a Voigt Profile. Mathematics (MDPI) 10 210. DOI: https://doi.org/10.3390/math10020210
[6] Thompson I (2024) Algorithm 1046: An Improved Recurrence Method for the Scaled Complex Error Function. ACM T. Math. Software 50. DOI: https://doi.org/10.1145/3688799
[7] Graham R L, Knuth D E and Patashnik O (2 1989) Concrete Mathematics, Addison-Wesley: Reading.
[8] The mpmath development team (2023) mpmath: a Python library for arbitrary-precision floating-point arithmetic (version 1.3.0). https://mpmath.org (2023).
[9] Faddeyeva V N and Terent’ev N M (1961) Tables of Values of the Function w(z) = ... for Complex Argument, Pergamon: Oxford.
[10] Gautschi W (1970) Efficient computation of the complex error function. SIAM J. Numer. Anal. 7 187. DOI: https://doi.org/10.1137/0707012
Published
Issue
Section
License
Copyright (c) 2025 Joachim Wuttke

This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.







