InvFD, an OCTAVE routine for the numerical inversion of the FermiDirac integral
Abstract
Given a value of the FermiDirac integral ∫ 0 ∞ t^{j}/dt ^{e t  η} + 1, this routine returns the value of the parameter η for a given j with a relative error less than 10^{13}. The inversion is provided for η ∈ [  30 , 100 ] and for the following set of j values, {  1 / 2 , 1 / 2 , 3 / 2 , 5 / 2 , 1 , 2 }. For η ∈ [  30 ,  2 ], an iterative method involving the McDougall and Stoner series is used. For the rest of the region of interest, a rational fit is employed.
 Publication:

Computer Physics Communications
 Pub Date:
 October 2021
 DOI:
 10.1016/j.cpc.2021.108062
 Bibcode:
 2021CoPhC.26708062M
 Keywords:

 FermiDirac integral;
 Inversion;
 McDougall and Stoner series;
 Rational approximation