Debye function: Difference between revisions

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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


:<math>F_j(x) = \frac{1}{\Gamma(j+1)} \int_0^\infty \frac{t^j}{\exp(t-x) + 1}\,dt.</math>


This is an alternate definition of the [[polylogarithm]] function. The closed form of the function exists for ''j''&nbsp;=&nbsp;0:
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:<math>F_0(x) = \ln(1+\exp(x)).\,</math>
 
== See also ==
* [[Incomplete Fermi–Dirac integral]]
* [[Gamma function]]
* Table of Integrals, Series, and Products, I.S. Gradshteyn, I.M. Ryzhik, 5th edition, p.&nbsp;370, formula № 3.411.3.
 
==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]
 
{{DEFAULTSORT:Complete Fermi-Dirac integral}}
[[Category:Special functions]]
 
 
{{mathanalysis-stub}}

Latest revision as of 09:30, 18 June 2014


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