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wrkdirs::usr...::man::voigt(3) libcerf manual wrkdirs::usr...::man::voigt(3) 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(-x^2/2/sigma^2) and a Lorentzian L(x,gamma) = |gamma| / pi / ( x^2 + gamma^2 ), 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. perl v5.36.3 2023-08-02 wrkdirs::usr...::man::voigt(3)
NAME | SYNOPSIS | DESCRIPTION | REFERENCES | SEE ALSO | AUTHORS | COPYING
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