Precision approximations for Fermi–Dirac functions of the integer index

Abstract

The Fermi–Dirac functions of the integer index are widely used in electron transport problems in dense substances. Polynomial approximations are constructed for their quick calculation. A simple algorithm yielding the coefficients of such approximations based on the interpolation with a special linear-trigonometric grid is developed. It is demonstrated that this grid gives almost optimal results. For the functions of indices 1, 2, and 3, the coefficients of such interpolations ensuring the relative error of 2 × 10⁻¹⁶ under 9 free parameters are obtained.