The expected distance from origin after a random walk of $N$ steps in a $d$ dimensional space, is close to $$\sqrt{\dfrac{2N}{d}}\dfrac{\Gamma\left(\dfrac{d+1}{2}\right)}{\Gamma\left(\dfrac{d}{2}\right)}$$ for very large $N$. This was mentioned here. I would be very obliged if someone can mention to me a reference (bibliographic) to an article, book or any publication, where this expression was derived or mentioned. Please restrict to references, and not explanation of the formula itself.
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$\begingroup$ The expression was given by "Henry" to a question by "Diego" in january 2012. Is it possible to have the source of this Formula? $\endgroup$– Picard PorathCommented Sep 1, 2013 at 11:36
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$\begingroup$ You might try to ping Henry under his answer, to see, whether he knows about a reference. $\endgroup$– Martin SleziakCommented Sep 1, 2013 at 12:22
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$\begingroup$ @ Martin Sleziak, thanks a lot. Unfortunately I am not qualified to add a comment to the old answer. Do you have an idea how can I contact Henry on the subject. Any help will be highly appreciated. $\endgroup$– Picard PorathCommented Sep 1, 2013 at 14:22
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3$\begingroup$ For those seeking for the reference > 4 years after the question was asked, here is a 2011 paper with explicit computations: pdfs.semanticscholar.org/8e6b/… $\endgroup$– Kolya IvankovCommented Dec 15, 2017 at 6:40
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