1builddir::build::BUILD::libbucielrdfd-ivlr1i:.b:1cb3eu:ri:flmdam:na::nB:uUwaI_lLoDf:_:zl(i3b)cerf-v1.13::man::w_of_z(3)
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NAME

6       w_of_z, im_w_of_x - Faddeeva's rescaled complex error function
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SYNOPSIS

9       #include <cerf.h>
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11       double _Complex w_of_z ( double _Complex z );
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13       double im_w_of_x ( double x );
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DESCRIPTION

16       Faddeeva's rescaled complex error function w(z), also called the plasma
17       dispersion function.
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19       w_of_z returns w(z) = exp(-z^2) * erfc(-i*z).
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21       im_w_of_x returns Im[w(x)].
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REFERENCES

24       To compute w(z), a combination of two algorithms is used:
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26       For sufficiently large |z|, a continued-fraction expansion similar to
27       those described by Gautschi (1970) and Poppe & Wijers (1990).
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29       Otherwise, Algorithm 916 by Zaghloul & Ali (2011), which is generally
30       competitive at small |z|, and more accurate than the Poppe & Wijers
31       expansion in some regions, e.g. in the vicinity of z=1+i.
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33       To compute Im[w(x)], Chebyshev polynomials and continous fractions are
34       used.
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36       Milton Abramowitz and Irene M. Stegun, "Handbook of Mathematical
37       Functions", National Bureau of Standards (1964): Formula (7.1.3)
38       introduces the nameless function w(z).
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40       Walter Gautschi, "Efficient computation of the complex error function,"
41       SIAM J. Numer. Anal. 7, 187 (1970).
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43       G. P. M. Poppe and C. M. J. Wijers, "More efficient computation of the
44       complex error function," ACM Trans. Math. Soft. 16, 38 (1990).
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46       Mofreh R. Zaghloul and Ahmed N. Ali, "Algorithm 916: Computing the
47       Faddeyeva and Voigt Functions," ACM Trans. Math. Soft. 38, 15 (2011).
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49       Steven G. Johnson, http://ab-initio.mit.edu/Faddeeva
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SEE ALSO

52       This function is used to compute several other complex error functions:
53       dawson(3), voigt(3), cerf(3), erfcx(3), erfi(3).
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55       Homepage: http://apps.jcns.fz-juelich.de/libcerf
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AUTHORS

58       Steven G. Johnson, http://math.mit.edu/~stevenj,
59         Massachusetts Institute of Technology,
60         researched the numerics, and implemented the Faddeeva function.
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62       Joachim Wuttke <j.wuttke@fz-juelich.de>, Forschungszentrum Juelich,
63         reorganized the code into a library, and wrote this man page.
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65       Please report bugs to the authors.
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COPYING

68       Copyright (c) 2012 Massachusetts Institute of Technology
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70       Copyright (c) 2013 Forschungszentrum Juelich GmbH
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72       Software: MIT License.
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74       This documentation: Creative Commons Attribution Share Alike.
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