Connected category: Difference between revisions

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In [[mathematics]], the '''Incomplete Polylogarithm''' function is related to the [[polylogarithm]] function. It is sometimes known as the [[incomplete Fermi–Dirac integral]] or the incomplete [[Bose–Einstein statistics|Bose–Einstein]] integral. It may be defined by:
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:<math>
\operatorname{Li}_s(b,z) = \frac{1}{\Gamma(s)}\int_b^\infty \frac{x^{s-1}}{e^x/z-1}~dx.
</math>
 
Expanding about z=0 and integrating gives a series representation:
 
:<math>
\operatorname{Li}_s(b,z) = \sum_{k=1}^\infty \frac{z^k}{k^s}~\frac{\Gamma(s,kb)}{\Gamma(s)}
</math>
 
where &Gamma;(s) is the [[gamma function]] and &Gamma;(s,x) is the upper [[incomplete gamma function]].
 
== References ==
* GNU Scientific Library - Reference Manual http://www.gnu.org/software/gsl/manual/gsl-ref.html#SEC117
 
[[Category:Special functions]]

Latest revision as of 10:33, 5 May 2014

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