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:

“Each of us is incomplete compared to someone else, an animal’s incomplete compared to a person ... and a person compared to God, who is complete only to be imaginary.”
—Georges Bataille (1897–1962)