# A Model for Fermi-Dirac Integrals

A Model for Fermi-Dirac Integrals

Fermi–Dirac integrals arise in calculating pressure and density in degenerate matter, such as neutron stars; they also occur in the electronic density of semiconductors. A (semi-)closed form was not known until 1995, when Howard Lee noticed the application of the integral form of polylogarithms. We developed an alternative expression, (η)=dx (plotted here), using an exponential model that is accurate for (arXiv:0909.3653v5 [math.GM]). Here we compare the model, in green, with the polylogarithm expression, in blue, for Fermi–Dirac integrals half-integer order , with (orders commonly used in astrophysics and semiconductors).

F

k/2

1

Γ1+

k

2

∞

∫

0

k/2

x

1+

x-η

e

η<3

k

2

k=-1,1,3,5