Simple way to the high-temperature expansion of relativistic Fermi-Dirac integrals

TL;DR

This paper derives a high-temperature expansion for the pressure and related thermodynamic quantities of a relativistic Fermi gas, providing a simplified analytical approach for such systems at elevated temperatures.

Contribution

It introduces a straightforward method to obtain high-temperature expansions of relativistic Fermi-Dirac integrals and related densities, enhancing analytical tools for relativistic thermodynamics.

Findings

Derived series expansion for pressure at high temperatures.

Expressed particle number, scalar, and entropy densities as derivatives of pressure.

Provides analytical formulas for relativistic Fermi gases in high-temperature regimes.

Abstract

The pressure of an ideal relativistic Fermi gas is computed as an infinite series for high temperatures at nonzero chemical potentials. The expansion of the particle number density, scalar density, and entropy density as first derivatives of the pressure is also found.