# erfc: Complementary error function In NORMT3: Evaluates complex erf, erfc, Faddeeva, and density of sum of Gaussian and Student's t

## Description

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

2/√{π} \int_{z}^{∞} \exp^{-t^2} dt

.

## Usage

 1 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.

erf

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 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.