1builddir::build::BUILD::libcbeurifl-dvld2ii.br1c::e::rbmfuainml:ad:n:vu:oaBilUgItL(D3:):libcerf-v2.1::man::voigt(3)
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NAME

6       voigt - Voigt's function, convolution of Gaussian and Lorentzian
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SYNOPSIS

9       #include <cerf.h>
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11       double voigt ( double x, double sigma, double gamma );
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DESCRIPTION

14       The function voigt returns Voigt's convolution
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16         voigt(x,sigma,gamma) = integral G(t,sigma) L(x-t,gamma) dt
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18       of a Gaussian
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20         G(x,sigma) = 1/sqrt(2*pi)/|sigma| * exp(-x^2/2/sigma^2)
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22       and a Lorentzian
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24         L(x,gamma) = |gamma| / pi / ( x^2 + gamma^2 ),
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26       with the integral extending from -infinity to +infinity.
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28       If sigma=0, L(x,gamma) is returned. Conversely, if gamma=0, G(x,sigma)
29       is returned.
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31       If sigma=gamma=0, the return value is Inf for x=0, and 0 for all other
32       x. It is advisable to test input arguments to exclude this irregular
33       case.
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REFERENCES

36       Formula (7.4.13) in Abramowitz & Stegun (1964) relates Voigt's
37       convolution integral to Faddeeva's function w_of_z, upon which this
38       implementation is based:
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40          voigt(x,sigma,gamma) = Re[w(z)] / sqrt(2*pi) / |sigma|
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42       with
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44          z = (x+i*|gamma|) / sqrt(2) / |sigma|.
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SEE ALSO

47       voigt_hwhm(3)
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49       Related complex error functions: w_of_z(3), dawson(3), cerf(3),
50       erfcx(3), erfi(3).
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52       Homepage: http://apps.jcns.fz-juelich.de/libcerf
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AUTHORS

55       Joachim Wuttke <j.wuttke@fz-juelich.de>, Forschungszentrum Juelich,
56         based on the w_of_z implementation by Steven G. Johnson,
57       http://math.mit.edu/~stevenj, Massachusetts Institute of Technology.
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59       Please report bugs to the authors.
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COPYING

62       Copyright (c) 2013 Forschungszentrum Juelich GmbH
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64       Software: MIT License.
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66       This documentation: Creative Commons Attribution Share Alike.
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70perl v5.36.0               builddi2r0:2:2b-u0i7l-d2:1:BUILD::libcerf-v2.1::man::voigt(3)
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