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wrkdirs::usr...::man::w_of_z(3)	libcerf	manual wrkdirs::usr...::man::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.

perl v5.36.3			  2023-08-02   wrkdirs::usr...::man::w_of_z(3)

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