[eindiran]

I see that on the page for "Bose-Einstein condensate", in the section "Derivation". I don't see it in the "Derivation" section on the "Bose-Einstein statistics" page, which is where I was hoping to see an explanation (of what it means that it showed up here).

But this page has some of the desired info: https://en.wikipedia.org/wiki/Polylogarithm#Integral_represe...

"For ''z'' = 1 the polylogarithm reduces to the Riemann zeta function:

\operatorname{Li}_s(1) = \zeta(s) \qquad (\operatorname{Re}(s)>1)"

And

"The polylogarithm can be expressed in term of the integral of the Bose-Einstein distribution:

\operatorname{Li}_{s}(z) = {1 \over \Gamma(s)} \int_0^\infty {t^{s-1} \over e^t/z-1} \,dt"

[jpmattia]

FWIW, I think the reason it does not show up on the "Bose-Einstein statistics" page: The zeta function is not so relevant to describing how the bosons populate states at particular energies, but zeta is relevant once you start summing/integrating over those populations (eg calculating expectation values.)