w_of_z(3) libcerf manual w_of_z(3)
NAME
w_of_z, im_w_of_x - Faddeeva's rescaled complex error function
SYNOPSIS
#include <cerf.h>
double _Complex w_of_z ( double _Complex z );
double im_w_of_x ( double x );
DESCRIPTION
Faddeeva's rescaled complex error function w(z), also called the plasma
dispersion function.
w_of_z returns w(z) = exp(-z^2) * erfc(-i*z).
im_w_of_x returns Im[w(x)].
REFERENCES
To compute w(z), a combination of two algorithms is used:
For sufficiently large |z|, a continued-fraction expansion similar to
those described by Gautschi (1970) and Poppe & Wijers (1990).
Otherwise, Algorithm 916 by Zaghloul & Ali (2011), which is generally
competitive at small |z|, and more accurate than the Poppe & Wijers
expansion in some regions, e.g. in the vicinity of z=1+i.
To compute Im[w(x)], Chebyshev polynomials and continous fractions are
used.
Milton Abramowitz and Irene M. Stegun, "Handbook of Mathematical
Functions", National Bureau of Standards (1964): Formula (7.1.3)
introduces the nameless function w(z).
Walter Gautschi, "Efficient computation of the complex error function,"
SIAM J. Numer. Anal. 7, 187 (1970).
G. P. M. Poppe and C. M. J. Wijers, "More efficient computation of the
complex error function," ACM Trans. Math. Soft. 16, 38 (1990).
Mofreh R. Zaghloul and Ahmed N. Ali, "Algorithm 916: Computing the
Faddeyeva and Voigt Functions," ACM Trans. Math. Soft. 38, 15 (2011).
Steven G. Johnson, http://ab-initio.mit.edu/Faddeeva
SEE ALSO
This function is used to compute several other complex error functions:
dawson(3), voigt(3), cerf(3), erfcx(3), erfi(3).
Homepage: http://apps.jcns.fz-juelich.de/libcerf
AUTHORS
Steven G. Johnson, http://math.mit.edu/~stevenj,
Massachusetts Institute of Technology,
researched the numerics, and implemented the Faddeeva function.
Joachim Wuttke <j.wuttke@fz-juelich.de>, Forschungszentrum Juelich,
reorganized the code into a library, and wrote this man page.
Please report bugs to the authors.
COPYING
Copyright (c) 2012 Massachusetts Institute of Technology
Copyright (c) 2013 Forschungszentrum Juelich GmbH
Software: MIT License.
This documentation: Creative Commons Attribution Share Alike.
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