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So, I've found on Stackexchange that: $$\mathbb{E} \left[ \mid S_n \mid \right]=\sqrt{\frac{2n}{d}}\frac{\Gamma (\frac{d+1}{2})}{\Gamma (\frac{d}{2})},$$ but I'm not sure if I can cite it in my thesis, like straight from someone's comment...

Do you know any book that provides this formula (even without proof)?

joriki
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Michał Dąbrowski
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    Why don't you prove it in your thesis ? it shouldn't be to difficult... – Surb Mar 28 '20 at 10:55
  • https://math.stackexchange.com/questions/103142/expected-value-of-random-walk – Mathphys meister Mar 28 '20 at 10:59
  • \mid is for use as a binary operator, e.g. divisibility (p\mid n$\to p\mid n$), or similar settings where spacing is needed, e.g. conditional probabilities (P(A\mid B) $\to P(A\mid B)$). For single norm bars, just use |. (For double norm bars there is \|.) Also, you can get properly sized parentheses (and other paired delimiters) that adjust to the size of their content by preceding them with \left and \right. More generally, here's a tutorial and reference for typesetting math on this site. – joriki Mar 28 '20 at 11:08
  • @Surb you're right, it's not difficult... but my thesis is already becoming too long for my uni standards and Random Walk is not the main theme of it so it would be nice to just add a cite there and continue ;) – Michał Dąbrowski Mar 28 '20 at 11:16

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