Fermi-Dirac Distribution

A distribution which arises in the study of half-integral spin particles in physics,

$$P(k) = {k^s\over e^{k-\mu}+1}.$$

Its integral is

$$\int_0^\infty {k^s\,dk\over e^{k-\mu}+1}=e^\mu \Gamma(s+1)\Phi(-e^\mu,s+1,1),$$

where $\Phi(z,s,a)$ is the Lerch Transcendent.