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#2 03. 09. 2013 13:56
Re: Integral of ceiling-floor function
Here is my trial of the first one.
1) Reducing the first integral into sum:
, but when
? That is if and only if there is 
such that
i.e. 
on intervals 
and is 
otherwise. Thus2) Non-rigorous computaion of the sum:
. It can be expressed as an infinite power series, with infinite radius of convergence, and thus it can be analyticaly continuated in whole 
. The zeros of 
are 
for 
and 
. Here comes the non-rigorous part - we will treat it as a polynomial and factorize it into ireducible terms over 
3) I don't have the rigorous method but here are some thoughts:
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#3 03. 09. 2013 18:45
Re: Integral of ceiling-floor function
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