Faddeeva function

Summary

The Faddeeva function is the scaled complex complementary error function $w(z) = e^{-z^2} \operatorname{erfc}(-iz)$. It is an entire function, and in the upper half-plane it is a Cauchy-type integral of the Gaussian. On the real line its real part is $e^{-x^2}$ and its imaginary part is a multiple of the Dawson function. It is used to compute the Voigt line profile in spectroscopy and complex error functions in numerical work.