 Polylogarithm

For $|z|<1$, the polylogarithm is ${\mathrm{Li}}_s(z)={\sum }_{n\ge 1}{z}^n/n^s$; contour formulas analytically continue it to a slit plane.

The polylogarithm is a special mathematical function denoted as \(\text{Li}_s(z)\), which generalizes the concept of logarithms to allow for the exponentiation of complex variables.