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Incomplete polylogarithm

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 integral. It may be defined by:

Li_s(b,z) = \frac{1}{\Gamma(s)}\int_b^\infty \frac{x^{s-1}}{e^x/z-1}~dx

Expanding about z=0 and integrating gives a series representation:

Li_s(b,z) = \sum_{k=1}^\infty \frac{z^k}{k^s}~\frac{\Gamma(s,kb)}{\Gamma(s)}

where Γ(s) is the gamma function and Γ(s,x) is the incomplete gamma function.

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Last updated: 05-29-2005 02:16:21
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