Complete Fermi–Dirac integral
From Infogalactic: the planetary knowledge core
In mathematics, the complete Fermi–Dirac integral, named after Enrico Fermi and Paul Dirac, for an index j is defined by
This equals
where is the polylogarithm.
Its derivative is
and this derivative relationship is used to define the Fermi-Dirac integral for nonpositive indices j.
Special values
The closed form of the function exists for j = 0:
See also
References
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External links
- GNU Scientific Library - Reference Manual
- Fermi-Dirac integral calculator for iPhone/iPad
- Notes on Fermi-Dirac Integrals
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