Definition:Polylogarithm

Definition

The polylogarithm $\map {\Li_s} z$ is defined on $\set {z \in \C: 0 \le \cmod z < 1, s \in \C} \cup \set {z = 1, \map \Re s > 1}$ as the series:

$\ds \map {\Li_s} z = \sum_{n \mathop = 1}^\infty \frac {z^n} {n^s}$

Also see

• The Riemann zeta function of which $\Li_s$ is a generalization
• The Lerch transcendent, of which $\Li_s$ is a special case

• Results about the polylogarithm can be found here.

Sources

• Weisstein, Eric W. "Polylogarithm." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Polylogarithm.html