# About the complex error function

1. Jul 8, 2008

### luisgml_2000

Hello!

I'm studying on my own the complex error function $$w(z)$$, also known as Faddeyeva function. On page 297 from Abramowitz it is stated that

$$\frac{i}{\pi} \int_0^{\infty} \frac{e^{-t^2}}{z-t}\, dt=e^{-z^2}\operatorname{erfc}(-iz)$$

where

$$\operatorname{erfc}(z)=\frac{2}{\sqrt{\pi}}\int_z^\infty e^{-t^2} \, dt$$

The former identity is puzzling me and therefore I can't come up with a proof for it. Welcome any suggestions!