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: 318

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

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8. W. Voigt, Uber das Gesetz der Intensitatsverteilung innerhalb der Linien eines Gasspektrums, Sitzungsber. Bayer. Akad. Wiss. Math.-Naturwiss. Kl. 25 (1912), pp. 603-620. https://publikationen.badw.de/de/003395768

9. Y. Wang, B. Zhou, R. Zhao, B. Wang, Q. Liu, M. Dai, Super-Accuracy Calculation for the Half Width of a Voigt Profile, Mathematics 10 (2022), no. 210 (14 pages). https://doi.org/10.3390/math10020210 DOI: https://doi.org/10.3390/math10020210

10. J. Wuttke, A. Kleinsorge, Algorithm 1xxx: Code generation for piecewise Chebyshev approximation, submitted to ACM TOMS. DOI: https://doi.org/10.1145/3805698

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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