On Saturday, December 6, 2014 4:30:35 PM UTC+1, bluescarni wrote:
>
> - I imagine if you calculate it as an elliptic integral (say, using the 
> Weierstrassian functions) you would end up with elliptic invariants g1 and 
> g2 with special values that make the elliptic integral collapse to an 
> elementary function?
>

Define elementary.  I guess the integral is a holonomic function. 
x/(exp(x)-1) is not, though it looks quite elementary.

https://en.wikipedia.org/wiki/Holonomic_function

Just a guess.

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