Precise and fast computation of inverse Fermi-Dirac integral of order 1/2 by minimax rational function approximation

DOI10.1016/j.amc.2015.03.015zbMath1464.65023OpenAlexW1972648206MaRDI QIDQ1636894

Toshio Fukushima

Publication date: 7 June 2018

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

Full work available at URL: https://doi.org/10.1016/j.amc.2015.03.015

zbMATH Keywords

function approximationFermi-Dirac integralrational function approximationminimax approximationinverse Fermi-Dirac integral

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Computation of special functions and constants, construction of tables (65D20) Statistical mechanics of solids (82D20) Approximation algorithms (68W25) Numerical integration (65D30)

Related Items (3)

InvFD, an OCTAVE routine for the numerical inversion of the Fermi-Dirac integral ⋮ Rational function approximation of Hardy space on half strip ⋮ The application of real convolution for analytically evaluating Fermi-Dirac-type and Bose-Einstein-type integrals

Uses Software

• Mathematica
• Fermi-Dirac
• DLMF

Cites Work

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• Analytical computation of generalized Fermi-Dirac integrals by truncated Sommerfeld expansions
• Double exponential formulas for numerical integration
• Precise and fast computation of Fermi-Dirac integral of integer and half integer order by piecewise minimax rational approximation
• 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
• Rational Chebyshev approximations for Fermi-Dirac integrals of orders -1/2, 1/2 and 3/2
• The Electric Conductivity of Simple Semiconductors

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