build::libcerf::src::libcerf::man::erfi(3)

NAME
cerfi, erfi - imaginary error function

SYNOPSIS
#include <cerf.h>

double _Complex cerfi ( double _Complex z );

double erfi ( double x );

DESCRIPTION
The function cerfi returns an error function rotated in the complex plane, erfi(z) = -i erf(iz).

The function erfi takes a real argument and returns a real result.

ACCURACY
Errors are given in units of eps = 2^-53 = 1.1e-16, as relative deviations from high-precision reference values; for complex results, of the modulus.

erfi(x) = exp(x^2) Im w(x) is computed from im_w_of_x(3). The argument x^2 of the exponential is rounded before the exponential is taken, so that the relative error grows like x^2 eps: it stays below 3 eps for |x| < 1 and reaches about 500 eps at |x| = 24. For |x| > 26.64 the result overflows to +-Inf.

cerfi(z) = -i erf(iz) inherits the accuracy of cerf(3): the relative error of the modulus stays below about 1.6 |z|^2 eps + 5 eps, except near the zeros of erfi, the first of which lie at z = +-1.8809 +- 1.4506i, where it is amplified without bound, and close to the origin, for 0.01 < |z| < 0.1 off the coordinate axes, where up to about 120 eps were found.

SEE ALSO
The implementation of cerfi and erfi is trivially based on the functions cerf(3) and im_w_of_x(3).

Other complex error functions in libcerf: dawson(3), erfcx(3), voigt(3), w_of_z(3).

The real error function comes with recent versions of glibc, as requested by the C99 standard: erf(3).

Homepage: https://jugit.fz-juelich.de/mlz/lib/cerf

AUTHORS
Steven G. Johnson, Massachusetts Institute of Technology,
  wrote this function as part of the MIT Faddeeva package.

Joachim Wuttke, Forschungszentrum Juelich,
  reorganized the code into a library, and wrote this man page.

CONTACT
Please report bugs to the maintainer:

Joachim Wuttke <j.wuttke@fz-juelich.de>

COPYING
Copyright (c) 2012 Massachusetts Institute of Technology

Copyright (c) 2013 Forschungszentrum Juelich GmbH

Software: MIT License.

This documentation: Creative Commons Attribution Share Alike.