Approximations to the Fermi Integrals and their Inverse:

Fermi integrals and their inverse functions cannot be analytically presented in finite form, with exception of a few special cases. The approximation of these functions is covered rather extensively in literature. The approaches ranges from crude, but simple formulas with proper asymptotic behaviors [475][416], over the classical approximations reviewed in comprehensive work [35], to novel general expressions of very high accuracy [147][90][89].

Most of the published works on this subject are listed in the following table:

[420][85][18] and [35] (review of results for til 1982)

[420][85]

[333][317][316][315][35]

[85][18]

very general approximations for the integrals [147][90][89] and their inverse functions [147] are recently developed.

In calculations carried out in this work, we employed simple expressions

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for and those proposed by Aymerich-Humet et al. in [18].

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Nilsson's expression for [333]