Classical, Fermi-Dirac, and Bose-Einstein statistics involve integrals that can be shown to be equivalent to polylogarithms. Polylogs have a particular simple series form:
$$ \text{Li}_s(x)=\sum_{n=1}^\infty \frac{x^n}{n^s} $$ For $x=\pm1$ and positive integer $s$ these equate to frequently-used constants. However, in many physics problems, $s$ is half-integer, and $x$ is large and negative. For $x$ large and negative, you can't use the series anymore, but an asymptotic formula or analytic continuation will work for calculation.