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I came across this integration in my studies.

$\int_{-\infty}^{\infty}|F((w_\textbf{_} - \hat{w_\textbf{_}})\tau) |^2 . d\tau$

It uses the Faddeeva function which is $F(z) = e^{-z^2}erfc(-iz)$. I am unsure how to integrate this equation since it contains this function. I searched online for quite a while but could not find any information pertaining to my problem. Can someone point me in the right direction to solve this integral?

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  • $\begingroup$ Is it possible to replace $w_{\textbf{_}} - \hat{w_\textbf{_}}$ by $a$? $\endgroup$
    – Alexey Ustinov
    Nov 22, 2014 at 5:27
  • $\begingroup$ Yes it is possible, I just wrote out the statement for completeness. $\endgroup$
    – user2958395
    Nov 22, 2014 at 5:38
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    $\begingroup$ After $t=a\tau$ you will get $I(a)=c/a$, where $c=I(1)$. $\endgroup$
    – Alexey Ustinov
    Nov 22, 2014 at 6:21
  • $\begingroup$ What is the function $I$? $\endgroup$
    – user2958395
    Nov 22, 2014 at 6:26
  • $\begingroup$ $I(a)=\int_{-\infty}^{\infty}|F(a\tau) |^2 d\tau$ $\endgroup$
    – Alexey Ustinov
    Nov 22, 2014 at 7:04

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