A generalized approximation of the Fermi–Dirac integrals

An analytical approximation for the Fermi–Dirac integral F j(η) for real j is proposed. This approximation works for −∞< η < ∞, with an error of 1.2% for −1/2< j < 1/2 and 0.7% for 1/2 < j < 5/2. The error increases with j for higher j values.