- #1
luisgml_2000
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Hello!
I'm studying on my own the complex error function [tex]w(z)[/tex], 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
[tex]
\operatorname{erfc}(z)=\frac{2}{\sqrt{\pi}}\int_z^\infty e^{-t^2} \, dt
[/tex]
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.
I'm studying on my own the complex error function [tex]w(z)[/tex], 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
[tex]
\operatorname{erfc}(z)=\frac{2}{\sqrt{\pi}}\int_z^\infty e^{-t^2} \, dt
[/tex]
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.
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