1builddir::build::BUILD::libbcueirlfd-dvli2ir.b:1c::eb:rumfialnmd:a::n:wuB_aUolIfL_Dz:(:3l)ibcerf-v2.1::man::w_of_z(3)
2
3
4

NAME

6       w_of_z, im_w_of_x - Faddeeva's rescaled complex error function
7

SYNOPSIS

9       #include <cerf.h>
10
11       double _Complex w_of_z ( double _Complex z );
12
13       double im_w_of_x ( double x );
14

DESCRIPTION

16       Faddeeva's rescaled complex error function w(z), also called the plasma
17       dispersion function.
18
19       w_of_z returns w(z) = exp(-z^2) * erfc(-i*z).
20
21       im_w_of_x returns Im[w(x)].
22

REFERENCES

24       To compute w(z), a combination of two algorithms is used:
25
26       For sufficiently large |z|, a continued-fraction expansion similar to
27       those described by Gautschi (1970) and Poppe & Wijers (1990).
28
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.
32
33       To compute Im[w(x)], Chebyshev polynomials and continous fractions are
34       used.
35
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).
39
40       Walter Gautschi, "Efficient computation of the complex error function,"
41       SIAM J. Numer. Anal. 7, 187 (1970).
42
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).
45
46       Mofreh R. Zaghloul and Ahmed N. Ali, "Algorithm 916: Computing the
47       Faddeyeva and Voigt Functions," ACM Trans. Math. Soft. 38, 15 (2011).
48
49       Steven G. Johnson, http://ab-initio.mit.edu/Faddeeva
50

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).
54
55       Homepage: http://apps.jcns.fz-juelich.de/libcerf
56

AUTHORS

58       Steven G. Johnson, http://math.mit.edu/~stevenj,
59         Massachusetts Institute of Technology,
60         researched the numerics, and implemented the Faddeeva function.
61
62       Joachim Wuttke <j.wuttke@fz-juelich.de>, Forschungszentrum Juelich,
63         reorganized the code into a library, and wrote this man page.
64
65       Please report bugs to the authors.
66

COPYING

68       Copyright (c) 2012 Massachusetts Institute of Technology
69
70       Copyright (c) 2013 Forschungszentrum Juelich GmbH
71
72       Software: MIT License.
73
74       This documentation: Creative Commons Attribution Share Alike.
75
76
77
78perl v5.36.0              builddir2:0:2b2u-i0l7d-:2:1BUILD::libcerf-v2.1::man::w_of_z(3)
Impressum