Asymptotic Expansion of a Class of Fermi–Dirac Integrals

A procedure is presented for obtaining the complete asymptotic expansion of a class of fractional integrals (of Riemann–Liouville type), in which the integrand contains the product of two derivatives of the Fermi–Dirac integral. The procedure uses two-sided Laplace transforms and Abelian asymptotics of the inverse Laplace transform. The fractional integrals considered arise in various problems from statistical mechanics and solid state physics.