erfc: Complementary error function

In NORMT3: Evaluates Complex Erf, Erfc, Faddeeva, and Density of Sum of Gaussian and Student's t

Complementary error function

Description

Computes the complementary error function of a (possibly) complex valued argument. This function is

2/√{π} \int_{z}^{∞} \exp^{-t^2} dt

.

Usage

erfc(z)

Arguments

z	Argument of complementary error function

Details

Computes the complementary error function of a (possibly) complex valued argument. This function is

2/√{π} \int_{z}^{∞} \exp^{-t^2} dt

This function actually calls FORTRAN code (algorithm TOMS 680) which computes the Faddeeva's function and then with a slight modification obtains the erfc function of a complex-valued argument.

Value

The complementary error function of z

Author(s)

Guy P. Nason, Department of Mathematics, University of Bristol

References

Poppe, G.P.M. and Wijers, C.M.J. (1990) More efficient computation of the complex error function. ACM Transactions on Mathematical Software, 16, 38–46.

See Also

erf

Examples

erfc(0)
#
# Should give 1
#
erfc(1)
#
# Should give 0.1572992+0i
#
erfc(complex(re=1, im=1))
#
# Should give -0.3161513-0.1904535i
#

NORMT3 documentation built on April 25, 2022, 5:06 p.m.