The Fermi-Dirac functions. Properties of functions

The Fermi–Dirac functions of an arbitrary real index are considered. An overview of their most important properties is presented, including function expansions with negative and positive arguments. The series is built, which converges for all values of the argument. The coefficients of this series for integer and half-integer function indices are calculated. The analogous properties are investigated for the integral Fermi–Dirac function.