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:

$\operatorname{Li}_s(b,z) = \frac{1}{\Gamma(s)}\int_b^\infty \frac{x^{s-1}}{e^x/z-1}~dx.$

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

$\operatorname{Li}_s(b,z) = \sum_{k=1}^\infty \frac{z^k}{k^s}~\frac{\Gamma(s,kb)}{\Gamma(s)}$

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

Famous quotes containing the word incomplete:

“The real weakness of England lies, not in incomplete armaments or unfortified coasts, not in the poverty that creeps through sunless lanes, or the drunkenness that brawls in loathsome courts, but simply in the fact that her ideals are emotional and not intellectual.”
—Oscar Wilde (1854–1900)