erfc: Complementary error function

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

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

2/√{π} \int_{z}^{∞} \exp^{-t^2} dt

.

Usage

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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

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

Example output

NORMT3: Evaluates erf, erfc, Faddeeva functions and Gaussian/T sum densities
Copyright: Guy Nason 2005-2012
[1] 1+0i
[1] 0.1572992+0i
[1] -0.3161513-0.1904535i

NORMT3 documentation built on May 1, 2019, 8:05 p.m.

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