Complete Fermi-Dirac integral

In mathematics, the complete Fermi-Dirac integral for an index j is given by

$F_j(x) = \frac{1}{\Gamma(j+1)} \int_0^\infty \frac{t^j}{\exp(t-x) + 1}\,dt.$

This is an alternate definition of the polylogarithm function. The closed form of the function exists for $j = 0$ :

F 0 (x) = log(1 + exp(x))

[edit] See also

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