Analytical computation of generalized Fermi-Dirac integrals by truncated Sommerfeld expansions

DOI10.1016/J.AMC.2014.02.053zbMath1305.82058OpenAlexW2145953004MaRDI QIDQ470807

Toshio Fukushima

Publication date: 13 November 2014

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.02.053

zbMATH Keywords

Riemann zeta functiongeneralized Fermi-Dirac integralFermi-Dirac integralSommerfeld expansion

Mathematics Subject Classification ID

Statistical mechanics of solids (82D20) Numerical integration (65D30)

Related Items (6)

Computation of a general integral of Fermi-Dirac distribution by McDougall-Stoner method ⋮ Precise and fast computation of inverse Fermi-Dirac integral of order 1/2 by minimax rational function approximation ⋮ Precise and fast computation of Fermi-Dirac integral of integer and half integer order by piecewise minimax rational approximation ⋮ InvFD, an OCTAVE routine for the numerical inversion of the Fermi-Dirac integral ⋮ Precise and fast computation of generalized Fermi-Dirac integral by parameter polynomial approximation ⋮ Complete asymptotic expansions for the relativistic Fermi-Dirac integral

Uses Software

• Fermi-Dirac
• DLMF
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Cites Work

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• Double exponential formulas for numerical integration
• A Gaussian quadrature for the calculation of generalized Fermi-Dirac integrals
• On the computation of generalized Fermi-Dirac and Bose-Einstein integrals
• On the numerical evaluation of the generalised Fermi-Dirac integrals
• Gaussian integration with rescaling of abscissas and weights
• An IMT-type quadrature formula with the same asymptotic performance as the DE formula
• The Fermi-Dirac integrals $$\mathcal{F}_p (\eta ) = (p!)^{ - 1} \int\limits_0^\infty {\varepsilon ^p (e^{\varepsilon - \eta } + 1} )^{ - 1} d\varepsilon $$
• Algorithm 779: Fermi-Dirac functions of order -1/2, 1/2, 3/2, 5/2
• Fermi-Dirac functions of integral order
• Generalized Fermi-Dirac functions and derivatives: Properties and evaluation
• An accurate method for the generalized Fermi-Dirac integral

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