Power series for the half width of the Voigt function, rederived

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DOI:

https://doi.org/10.33993/jnaat542-1640

Keywords:

Voigt function, Faddeeva function, Maclaurin series, asymptotic series, high-precision computation
Abstract views: 3

Abstract

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.

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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

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Published

2025-12-15

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How to Cite

Wuttke, J. (2025). Power series for the half width of the Voigt function, rederived. J. Numer. Anal. Approx. Theory, 54(2), 345-356. https://doi.org/10.33993/jnaat542-1640