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| | In [[mathematics]], the '''complete Fermi–Dirac integral''', named after [[Enrico Fermi]] and [[Paul Dirac]], for an index ''j '' is given by |
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| | :<math>F_j(x) = \frac{1}{\Gamma(j+1)} \int_0^\infty \frac{t^j}{\exp(t-x) + 1}\,dt.</math> |
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| | This is an alternate definition of the [[polylogarithm]] function. The closed form of the function exists for ''j'' = 0: |
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| | :<math>F_0(x) = \ln(1+\exp(x)).\,</math> |
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| | == See also == |
| | * [[Incomplete Fermi–Dirac integral]] |
| | * [[Gamma function]] |
| | * Table of Integrals, Series, and Products, I.S. Gradshteyn, I.M. Ryzhik, 5th edition, p. 370, formula № 3.411.3. |
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| | ==External links== |
| | * [http://www.gnu.org/software/gsl/manual/gsl-ref.html#SEC117 GNU Scientific Library - Reference Manual] |
| | * [http://itunes.apple.com/us/app/fermi-dirac-integral-calculator/id446595443?mt=8&ls=1 Fermi-Dirac integral calculator for iPhone/iPad] |
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| | {{DEFAULTSORT:Complete Fermi-Dirac integral}} |
| | [[Category:Special functions]] |
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| | {{mathanalysis-stub}} |
In mathematics, the complete Fermi–Dirac integral, named after Enrico Fermi and Paul Dirac, for an index j is given by
This is an alternate definition of the polylogarithm function. The closed form of the function exists for j = 0:
See also
External links
Template:Mathanalysis-stub