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1: 7.19 Voigt Functions
§7.19 Voigt Functions
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§7.19(i) Definitions
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β–ΊSee accompanying textβ–Ί
Figure 7.19.1: Voigt function 𝖴 ⁑ ( x , t ) , t = 0.1 , 2.5 , 5 , 10 . Magnify
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β–ΊSee accompanying textβ–Ί
Figure 7.19.2: Voigt function 𝖡 ⁑ ( x , t ) , t = 0.1 , 2.5 , 5 , 10 . Magnify
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§7.19(iii) Properties
2: 7.21 Physical Applications
β–ΊVoigt functions 𝖴 ⁑ ( x , t ) , 𝖡 ⁑ ( x , t ) , can be regarded as the convolution of a Gaussian and a Lorentzian, and appear when the analysis of light (or particulate) absorption (or emission) involves thermal motion effects. …
3: 7.22 Methods of Computation
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§7.22(iv) Voigt Functions
4: 7.23 Tables
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  • Abramowitz and Stegun (1964, Table 27.6) includes the Goodwin–Staton integral G ⁑ ( x ) , x = 1 ⁒ ( .1 ) ⁒ 3 ⁒ ( .5 ) ⁒ 8 , 4D; also G ⁑ ( x ) + ln ⁑ x , x = 0 ⁒ ( .05 ) ⁒ 1 , 4D.

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

  • 5: 7.1 Special Notation
    β–ΊThe main functions treated in this chapter are the error function erf ⁑ z ; the complementary error functions erfc ⁑ z and w ⁑ ( z ) ; Dawson’s integral F ⁑ ( z ) ; the Fresnel integrals β„± ⁑ ( z ) , C ⁑ ( z ) , and S ⁑ ( z ) ; the Goodwin–Staton integral G ⁑ ( z ) ; the repeated integrals of the complementary error function i n ⁒ erfc ⁑ ( z ) ; the Voigt functions 𝖴 ⁑ ( x , t ) and 𝖡 ⁑ ( x , t ) . …
    6: Bibliography Z
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  • M. R. Zaghloul and A. N. Ali (2011) Algorithm 916: computing the Faddeyeva and Voigt functions. ACM Trans. Math. Software 38 (2), pp. Art. 15, 22.
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  • M. R. Zaghloul (2016) Remark on “Algorithm 916: computing the Faddeyeva and Voigt functions”: efficiency improvements and Fortran translation. ACM Trans. Math. Softw. 42 (3), pp. 26:1–26:9.
  • 7: Bibliography
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  • B. H. Armstrong (1967) Spectrum line profiles: The Voigt function. J. Quant. Spectrosc. Radiat. Transfer 7, pp. 61–88.
  • 8: Bibliography L
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  • A. E. Lynas-Gray (1993) VOIGTL – A fast subroutine for Voigt function evaluation on vector processors. Comput. Phys. Comm. 75 (1-2), pp. 135–142.
  • 9: Bibliography W
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  • R. J. Wells (1999) Rapid approximation to the Voigt/Faddeeva function and its derivatives. J. Quant. Spect. and Rad. Transfer 62 (1), pp. 29–48.
  • 10: 7.25 Software
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    §7.25(ii) erf ⁑ x , erfc ⁑ x , i n ⁒ erfc ⁑ ( x ) , x ℝ
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    §7.25(iii) erf ⁑ z , erfc ⁑ z , w ⁑ ( z ) , z β„‚
    β–ΊNo research software has been found for these functions. … β–Ί
    §7.25(vi) β„± ⁑ ( x ) , G ⁑ ( x ) , 𝖴 ⁑ ( x , t ) , 𝖡 ⁑ ( x , t ) , x ℝ
    β–ΊNo research software has been found for these functions. …