build::libcerf::src::libcerf-v2.4::man::cerf(3) libcerf manual build::libcerf::src::libcerf-v2.4::man::cerf(3)

cerf, cerfc - complex error functions

#include <cerf.h>

double _Complex cerf ( double _Complex z );

double _Complex cerfc ( double _Complex z );

The function cerf is the complex version of the error function: erf(z) = 2/sqrt(pi) * integral from 0 to z of exp(-t*t) dt.

The complementary complex error function cerfc is defined as erfc(z) = 1-cerf(z).

The computations are based on Faddeeva's function w_of_z(3).

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

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


Steven G. Johnson,,
Massachusetts Institute of Technology,
researched the numerics, and implemented the Faddeeva function.

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

Please report bugs to the authors.

Copyright (c) 2012 Massachusetts Institute of Technology

Copyright (c) 2013 Forschungszentrum Juelich GmbH

Software: MIT License.

This documentation: Creative Commons Attribution Share Alike.

2023-08-02 perl v5.36.1