AbstractBy means of a piecewise cubic Hermitian polynomial approximation and a theorem for the asymptotics used in our previous papers, an accurate expression for the generalized Fermi‐Dirac integral ℱ (z), derived from a Kane nonparabolic dispersion relation, for any values of reduced Fermienergy z and for the dimensionless conduction‐band nonparabolicity parameter β in the interval [0, 0.1493], is investigated witha precision of the order of 2 × 10−7. Then, two short seriesrepresentations for ℱ (z) are also presented and discussed. These accurate values of ℱ (z) (or reduced carrier density u(z) are used to evaluate the error of our two approximate expressions for z(u), appropriate to the lightly degenerate and degenerate cases, z≤4 and z≥4, respectively, and accurate within 0.5%. Finally, taking account of both the electron‐electron interaction effect and the spin‐orbit splitting interaction effect, the reduced Fermi energy z(u) and the electron effective mass in n‐type heavily doped GaAs crystals at 4.2 and 300 K are determined. Their numerical results are also compared with existing experimental results.