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Anyone know how to integrate the following?

$$ \int_0^{+\infty} \! e^{-t^2} \, \mathrm{d}t $$

Thanks

chengcj
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  • Thanks for answering and sorry for duplicating the question. – chengcj May 28 '15 at 13:01
  • BTW I used this once as Turing test on the Google recruiter, after he send me email that was obivously a template, where the substitution had not worked. – mvw May 28 '15 at 13:15
  • By the way, I'm new to math stack exchange. How did you guys find out that this question was duplicated? Is there a clever way to search for equations / formulae in math stack exchange? Thanks. – chengcj May 28 '15 at 14:23
  • I searched for "exp" and "e^" within my answers. You could try "e^{-t^2}" (with quotes) in the search box on the top right of the page. – mvw May 28 '15 at 14:27

1 Answers1

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See this paper link. In short: Go for the square, switch from rectangular to spherical summation, using spherical coordinates ("Trick of Poisson").

Note: Here is a slightly different version of the problem: link. It does not go to spherical coordinates explicitly but notes that the difference between integration over a square and over a circle vanishes for the dimensions going infinite.

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mvw
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