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About the complex error function

  1. Jul 8, 2008 #1

    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)


    \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.
  2. jcsd
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