erfcw

erfcw (z )

The erfcw is a complex form of the error function defined by

$$\displaystyle \operatorname{erfcw}(z)=\exp \left[-z^{2}\right] \operatorname{erfc}(-i z),$$

where

$$\displaystyle \operatorname{erfc}(z)=\frac{2}{\sqrt{\pi}} \int_{z}^{\infty} \exp \left[-t^{2}\right] d t.$$

The function is computed with accuracy of 0.5e-10. It is particularly useful for large |z| where the computation of erfc(z) starts encountering numerical instability.

References

1. http://en.wikipedia.org/wiki/Error_function

2. W. Gautschi, "Efficient Computation of the Complex Error Function", SIAM J. Numer. Anal. Vol. 7, No. 1, March 1970.

See Also

erf, erfc, erfcx, inverseErfc, dawson