About the complex error function

[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!

Thanks in advance for your attention.

 

[fresh_42]

This might help: https://arxiv.org/pdf/1601.01261.pdf
At least it contains the reference to the original paper, [1].
Or look at
https://www.nag.co.uk/doc/techrep/pdf/tr4_16.pdf