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.\" ========================================================================
.\"
.IX Title "voigt 3"
.TH voigt 3 "2013-03-11" "perl v5.14.2" "libcerf manual"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
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.SH "NAME"
voigt \- Voigt's function, convolution of Gaussian and Lorentzian
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
\&\fB#include <cerf.h\fR>
.PP
\&\fBdouble voigt ( double x, double sigma, double gamma );\fR
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
The function \fBvoigt\fR returns Voigt's convolution
.PP
.Vb 1
\&  voigt(x,sigma,gamma) = integral G(t,sigma) L(x\-t,gamma) dt
.Ve
.PP
of a Gaussian
.PP
.Vb 1
\&  G(x,sigma) = 1/sqrt(2*pi)/|sigma| * exp(\-x^2/2/sigma^2)
.Ve
.PP
and a Lorentzian
.PP
.Vb 1
\&  L(x,gamma) = |gamma| / pi / ( x^2 + gamma^2 ),
.Ve
.PP
with the integral extending from \-infinity to +infinity.
.PP
If sigma=0, L(x,gamma) is returned. Conversely, if gamma=0, G(x,sigma) is returned.
.PP
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.
.SH "RESOURCES"
.IX Header "RESOURCES"
Project web site: http://apps.jcns.fz\-juelich.de/libcerf
.SH "REFERENCES"
.IX Header "REFERENCES"
Formula (7.4.13) in Abramowitz & Stegun (1964) relates Voigt's convolution integral to Faddeeva's function \fBw_of_z\fR, upon which this implementation is based:
.PP
.Vb 1
\&   voigt(x,sigma,gamma) = Re[w(z)] / sqrt(2*pi) / |sigma|
.Ve
.PP
with
.PP
.Vb 1
\&   z = (x+i*|gamma|) / sqrt(2) / |sigma|.
.Ve
.SH "BUG REPORTS"
.IX Header "BUG REPORTS"
Please report bugs to the authors.
.SH "AUTHORS"
.IX Header "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.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
Related complex error functions in liberfc:
.PP
\&\fB\f(BIw_of_z\fB\|(3)\fR, \fB\f(BIdawson\fB\|(3)\fR, \fB\f(BIcerf\fB\|(3)\fR, \fB\f(BIerfcx\fB\|(3)\fR, \fB\f(BIerfi\fB\|(3)\fR.
.SH "COPYING"
.IX Header "COPYING"
Copyright (c) 2013 Forschungszentrum Juelich GmbH
.PP
Software: \s-1MIT\s0 License.
.PP
This documentation: Creative Commons Attribution Share Alike.