Complete asymptotic expansions of the Fermi–Dirac integrals Fp(η)=1/Γ(p+1)∫∞[εp/(1+eε−η)]dε

DOI10.1063/1.1350634zbMath1061.33021OpenAlexW1487492563MaRDI QIDQ2774867

Timothy M. Garoni, N. E. Frankel, M. Lawrence Glasser

Publication date: 26 February 2002

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1350634

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Other functions defined by series and integrals (33E20) Statistical mechanics of gases (82D05)

Related Items (5)

Precise and fast computation of Fermi-Dirac integral of integer and half integer order by piecewise minimax rational approximation ⋮ Improved analytical representation of combinations of Fermi-Dirac integrals for finite-temperature density functional calculations ⋮ InvFD, an OCTAVE routine for the numerical inversion of the Fermi-Dirac integral ⋮ Complete asymptotic expansions for the relativistic Fermi-Dirac integral ⋮ The application of real convolution for analytically evaluating Fermi-Dirac-type and Bose-Einstein-type integrals

Cites Work

• The Fermi-Dirac integrals $$\mathcal{F}_p (\eta ) = (p!)^{ - 1} \int\limits_0^\infty {\varepsilon ^p (e^{\varepsilon - \eta } + 1} )^{ - 1} d\varepsilon $$
• Note on the Evaluation of Some Fermi Integrals

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