Timeline for Alternating sum of square roots of binomial coefficients

8 events

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Apr 13, 2017 at 12:58	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Jan 6, 2012 at 18:25	comment	added	GH from MO		Mark, thank you. I don't know how to make this argument work for any $\alpha \in (0,1)$ since in general the integral is more wildly oscillating. Well, we can restrict to rational $\alpha$ which makes the oscillation more regular. At any rate, you can find and download de Bruijn's book off the internet (link not given, to avoid charges of 'piracy').
Jan 6, 2012 at 17:55	comment	added	Mark Wildon		Thank you very much for this proof. I would accept your answer as well if I could. I was able to read all but the end of Section 6.6 of de Bruijn's book via Google Books. He considers the sum $c_n$ for general $\alpha \in (0,1)$, saying 'It should be admitted that this is not a very natural question, as non-integral powers of binomial coefficients do not frequently occur in mathematics. The main reason for its discussion here is, that it is a difficult problem with various interesting aspects'.
Jan 6, 2012 at 6:46	history	edited	GH from MO	CC BY-SA 3.0	Fixed some typos.
Jan 6, 2012 at 6:17	history	edited	GH from MO	CC BY-SA 3.0	deleted 31 characters in body
Jan 6, 2012 at 6:07	history	edited	GH from MO	CC BY-SA 3.0	added 110 characters in body
Jan 6, 2012 at 6:02	history	edited	GH from MO	CC BY-SA 3.0	added 10 characters in body
Jan 6, 2012 at 5:55	history	answered	GH from MO	CC BY-SA 3.0