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Fermi-Dirac Distribution

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

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

Its integral is

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

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




© 1996-9 Eric W. Weisstein
1999-05-26