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The Fermi-Dirac functions. (English) Zbl 0063.00141

From the text: In recent years various applications (connected with the Fermi-Dirac statistics of the functions \[ F(t) = \int_0^\infty \frac{\phi'(x)\,dx}{e^{x-t}+1} \] have been made to physical and astrophysical problems. J. L. B. Cooper [Philos. Mag., VII. Ser. 30, 187–189 (1940; Zbl 0026.31501, JFM 66.0503.01)] has recently given a new method for evaluating these functions when \(\phi'(x)=x^k\). In this note the author has worked out the corresponding case for any function \(\phi(x)\).

MSC:

33E20 Other functions defined by series and integrals
44A10 Laplace transform
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