Analytical approximation of the Fermi–Dirac integrals of half-integer and integer orders

We obtain continuous analytical expressions approximating the Fermi–Dirac integrals of orders $j=-1/2, 1/2, 1, 3/2, 2, 5/2, 3, 7/2$ in a convenient form for calculation with reasonable accuracy $(1\div4)\%$ in a wide range of the degeneration in this paper. An approach based on the least square method for approximation was used. The demands to the approximation of integrals, to the range of variation of order j and to the definitional domain are considered in terms of the use of Fermi–Dirac integrals to determine the properties of metals and semiconductors.