The Fermi-Dirac integrals $$\mathcal{F}_p (\eta ) = (p!)^{ - 1} \int\limits_0^\infty {\varepsilon ^p (e^{\varepsilon - \eta } + 1} )^{ - 1} d\varepsilon $$

DOI10.1007/BF02920379zbMath0077.23704OpenAlexW1998120895MaRDI QIDQ3242096

Robert Balson Dingle

Publication date: 1957

Published in: Applied Scientific Research, Section B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02920379

zbMATH Keywords

Mechanics of solids

Related Items (20)

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 ⋮ 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 ⋮ The Bose-Einstein integrals $$\mathcal{B}_p (\eta ) = (p!)^{ - 1} \int\limits_0^\infty {\varepsilon ^p (e^{\varepsilon - \eta } - 1} )^{ - 1} d\varepsilon $$ ⋮ On the Theory of the Peltier Heat Pump ⋮ An algorithm of calculating transport parameters of thermoelectric materials using single band model with optimized integration methods ⋮ Analytical computation of generalized Fermi-Dirac integrals by truncated Sommerfeld expansions ⋮ Complete asymptotic expansions for the relativistic Fermi-Dirac integral ⋮ A note on the Randles--Sevcik function from electrochemistry ⋮ Dependence of the Thermoelectric Figure of Merit on Energy Bandwidth ⋮ Critical resonance in the non-intersecting lattice path model ⋮ Complete asymptotic expansions of the Fermi–Dirac integrals Fp(η)=1/Γ(p+1)∫∞[εp/(1+eε−η)dε] ⋮ Two new series for the Fermi-Dirac integral ⋮ Evaluation of integrals and the Mellin transform ⋮ The application of real convolution for analytically evaluating Fermi-Dirac-type and Bose-Einstein-type integrals ⋮ Note on the Evaluation of Some Fermi Integrals ⋮ Rational Chebyshev approximations for Fermi-Dirac integrals of orders -1/2, 1/2 and 3/2

Cites Work

• The integrals $$\mathfrak{A}_p (x) = (p!)^{ - 1} \int\limits_0^\infty {\varepsilon ^p (\varepsilon + x} )^{ - 1} e^{ - \varepsilon } d\varepsilon $$ and $$\mathfrak{B}_p (x) = (p!)^{ - 1} \int\limits_0^\infty {\varepsilon ^p (\varepsilon + x} )^{ - 2} e^{ - \varepsilon } d\varepsilon $$ and their tabulationdϕ and their tabulation
• The computation of Fermi-Dirac functions
• Fermi-Dirac functions of integral order
• On Bose-Einstein Functions
• The evaluation of integrals containing a parameter
• Unnamed Item
• Unnamed Item

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