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.