Applied Scientific Research, Section B

, Volume 6, Issue 1, pp 225–239 | Cite as

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

  • R. B. Dingle


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.


Asymptotic Series Integer Order Differentiation Formula Positive Argument Negative Argument 
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Copyright information

© Martinus Nijhoff 1957

Authors and Affiliations

  • R. B. Dingle
    • 1
  1. 1.Department of PhysicsUniversity of Western AustraliaNedlandsAustralia

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