Rational Chebyshev approximations for Fermi-Dirac integrals of orders -1/2, 1/2 and 3/2

DOI10.1090/S0025-5718-67-99899-7zbMath0149.11905OpenAlexW2016097360MaRDI QIDQ5528131

William J. Cody, Henry C. Jun. Thacher

Publication date: 1967

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-67-99899-7

zbMATH Keywords

numerical analysis

Related Items (12)

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 ⋮ Improved analytical representation of combinations of Fermi-Dirac integrals for finite-temperature density functional calculations ⋮ On the very accurate numerical evaluation of the generalized Fermi-Dirac integrals ⋮ InvFD, an OCTAVE routine for the numerical inversion of the Fermi-Dirac integral ⋮ Operator representation of fermi-Dirac and Bose-Einstein integral functions with applications ⋮ Non-isothermal Smoluchowski-Poisson equations as a singular limit of the Navier-Stokes-Fourier-Poisson system ⋮ A note on the Randles--Sevcik function from electrochemistry ⋮ Two new series for the Fermi-Dirac integral ⋮ The application of real convolution for analytically evaluating Fermi-Dirac-type and Bose-Einstein-type integrals ⋮ A computation of Fermi-Dirac integrals by asymptotics and the Hermite corrector formula ⋮ Hyperbolicity in extended thermodynamics of Fermi and Bose gases

Cites Work

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• Rational Chebyshev approximation using interpolation
• The Fermi-Dirac integrals $$\mathcal{F}_p (\eta ) = (p!)^{ - 1} \int\limits_0^\infty {\varepsilon ^p (e^{\varepsilon - \eta } + 1} )^{ - 1} d\varepsilon $$
• Asymptotic expansions and converging factors I. General theory and basic converging factors
• On the computation of rational approximations to continuous functions
• An Approximation to the Fermi Integral F 1/2 (x)

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