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What is the most general way to compute (formally not numerically) the following integral:

$\int_\mathbb{R}\exp(iuz - \frac{(x-z)^2}{2t})dz, \space t>0$

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  • $\begingroup$ What do you mean by "most general". Typically, just complete the square and use the gaussian integral. $\endgroup$ – mickep Sep 4 '17 at 15:18
  • $\begingroup$ So, the standard way is to use "gaussian integral" ? Could you write the solution ? $\endgroup$ – arnold_107 Sep 4 '17 at 15:19
  • $\begingroup$ Oh, now I ser that there is also an $i$. Then One has to work a bit with paths, but essentially THE same gös through. I am afk, so someone else will probably help before I come back. $\endgroup$ – mickep Sep 4 '17 at 15:23
  • $\begingroup$ I recently did this in an answer to another question. Also read the comments! $\endgroup$ – md2perpe Sep 4 '17 at 19:34