Precise and fast computation of Fermi-Dirac integral of integer and half integer order by piecewise minimax rational approximation
type: Item
instance of: scholarly article
title: Precise and fast computation of Fermi-Dirac integral of integer and half integer order by piecewise minimax rational approximation
zbMATH Open document ID: 1464.65024
author: T. Fukushima
published in: Applied Mathematics and Computation
publication date: 2018-06-07T00:00:00Z
Mathematics Subject Classification ID: 65D30
Mathematics Subject Classification ID: 68W25
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 33E20
Mathematics Subject Classification ID: 82D20
zbMATH DE Number: 6881761
zbMATH Keywords: Chebyshev series expansion
zbMATH Keywords: Fermi-Dirac integral
zbMATH Keywords: Maclaurin series expansion
zbMATH Keywords: minimax rational approximation
zbMATH Keywords: Sommerfeld expansion
describes a project that uses: Algorithm 745
describes a project that uses: Mathematica
describes a project that uses: Digital Library of Mathematical Functions
MaRDI profile type: Publication
full work available at URL: j.amc.2015.03.009
OpenAlex ID: W1965569373
cites work: Q5395377
cites work: Q3579593
cites work: The Fermi-Dirac integrals $$\mathcal{F}_p (\eta ) = (p!)^{ - 1} \int\limits_0^\infty {\varepsilon ^p (e^{\varepsilon - \eta } + 1} )^{ - 1} d\varepsilon $$
cites work: Q5653524
cites work: Numerical inversion of a general incomplete elliptic integral
cites work: Algorithm 745: computation of the complete and incomplete Fermi-Dirac integral
cites work: Gaussian integration with rescaling of abscissas and weights
cites work: Fermi-Dirac functions of integral order
cites work: Rational Chebyshev approximations for Fermi-Dirac integrals of orders -1/2, 1/2 and 3/2
cites work: Algorithm 779: Fermi-Dirac functions of order -1/2, 1/2, 3/2, 5/2
cites work: Complete asymptotic expansions of the Fermi-Dirac integrals \(\mathcal F_ p(\eta)=1/\Gamma(p+1)\int^ \infty_ 0 [\epsilon^ p/(1+e^{\epsilon-\eta})]d\epsilon\).
cites work: Computation of a general integral of Fermi-Dirac distribution by McDougall-Stoner method
cites work: Q3592129
cites work: Double exponential formulas for numerical integration
cites work: Analytical computation of generalized Fermi-Dirac integrals by truncated Sommerfeld expansions
cites work: Some remarks on multivariate Chebyshev polynomials
cites work: Recursive computation of derivatives of elliptic functions and of incomplete elliptic integrals
cites work: Generalizations of Horner's Rule for Polynomial Evaluation
DOI: 10.1016/J.AMC.2015.03.009
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description: scientific article; zbMATH DE number 6881761