line broadening function

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1: 7.19 Voigt Functions

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7.19.4 $$H(a,u)=\frac{a}{\pi }{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{{\mathrm{e}}^{-t^2}dt}{{(u-t)}^2+a^2}=\frac{1}{a\sqrt{\pi }}𝖴(\frac{u}{a},\frac{1}{4a^2}).$$

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Defines:

$H(a,u)$: line-broadening function

Symbols:

$𝖴(x,t)$: Voigt function, $\pi$: the ratio of the circumference of a circle to its diameter, $dx$: differential of $x$ , $\mathrm{e}$: base of natural logarithm and $\int$: integral

Permalink:

http://dlmf.nist.gov/7.19.E4

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See also:

Annotations for §7.19(i), §7.19 and Ch.7

► $H(a,u)$ is sometimes called the line broadening function; see, for example, Finn and Mugglestone (1965). …

2: 7.23 Tables

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Finn and Mugglestone (1965) includes the Voigt function $H(a,u)$, $u\in [0,22]$, $a\in [0,1]$, 6S.

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3: Bibliography F

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Tables of the line broadening function $H(a,v)$ . Monthly Notices Roy. Astronom. Soc. 129, pp. 221–235.

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External Links:

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Referenced by:

§7.19(i), 3rd item.

Encodings:

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4: Bibliography P

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Fast analytic formulas for the modified Bessel functions of imaginary order for spectral line broadening calculations. J. Quantit. Spec. and Rad. Trans. 62 (4), pp. 389–395.

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External Links:

Document

Referenced by:

§10.76(ii).

Encodings:

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