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

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Applied Scientific Research, Section B

Summary

Following a discussion of the relationship of the Fermi-Dirac integrals to other functions, complete expansions are developed which enable the integrals of all orders to be calculated without recourse to numerical integration. In order to supplement existing tables, values are given for orders—1 and 0 for positive and negative arguments, and for orders 1, 2, 3, 4 for positive arguments.

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Authors and Affiliations

  1. Department of Physics, University of Western Australia, Nedlands, Australia

    R. B. Dingle

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  1. R. B. Dingle
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Additional information

This work was commenced in 1954 while the author held a Post-Doctorate Fellowship at the National Research Council, Ottawa. The later work was supported by the Research Grants Committee of the University of Western Australia.

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Dingle, R.B. The Fermi-Dirac integrals\(\mathcal{F}_p (\eta ) = (p!)^{ - 1} \int\limits_0^\infty {\varepsilon ^p (e^{\varepsilon - \eta } + 1} )^{ - 1} d\varepsilon \) . Appl. Sci. Res. 6, 225–239 (1957). https://doi.org/10.1007/BF02920379

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  • DOI: https://doi.org/10.1007/BF02920379

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