Man page - voigt(3)

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Manual

voigt

NAME
SYNOPSIS
DESCRIPTION
REFERENCES
SEE ALSO
AUTHORS
COPYING

NAME

voigt - Voigt’s function, convolution of Gaussian and Lorentzian

SYNOPSIS

#include <cerf.h >

double voigt ( double x, double sigma, double gamma );

DESCRIPTION

The function voigt returns Voigt’s convolution

voigt(x,sigma,gamma) = integral G(t,sigma) L(x-t,gamma) dt

of a Gaussian

G(x,sigma) = 1/sqrt(2*pi)/|sigma| * exp(-xˆ2/2/sigmaˆ2)

and a Lorentzian

L(x,gamma) = |gamma| / pi / ( xˆ2 + gammaˆ2 ),

with the integral extending from -infinity to +infinity.

If sigma=0, L(x,gamma) is returned. Conversely, if gamma=0, G(x,sigma) is returned.

If sigma=gamma=0, the return value is Inf for x=0, and 0 for all other x. It is advisable to test input arguments to exclude this irregular case.

REFERENCES

Formula (7.4.13) in Abramowitz & Stegun (1964) relates Voigt’s convolution integral to Faddeeva’s function w_of_z , upon which this implementation is based:

voigt(x,sigma,gamma) = Re[w(z)] / sqrt(2*pi) / |sigma|

with

z = (x+i*|gamma|) / sqrt(2) / |sigma|.

SEE ALSO

voigt_hwhm(3)

Related complex error functions: w_of_z(3) , dawson(3) , cerf(3) , erfcx(3) , erfi(3) .

Homepage: http://apps.jcns.fz-juelich.de/libcerf

AUTHORS

Joachim Wuttke <j.wuttke@fz-juelich.de>, Forschungszentrum Juelich,
based on the w_of_z implementation by Steven G. Johnson, http://math.mit.edu/˜stevenj, Massachusetts Institute of Technology.

Please report bugs to the authors.

COPYING

Copyright (c) 2013 Forschungszentrum Juelich GmbH

Software: MIT License.

This documentation: Creative Commons Attribution Share Alike.