Incomplete polylogarithm

The incomplete polylogarithm is a generalization of the polylogarithm function, which is defined as: \[ \text{Li}_s(z) = \sum_{n=1}^{\infty} \frac{z^n}{n^s} \] for complex numbers \( z \) and \( s \). The series converges for \( |z| < 1 \), and can be analytically continued beyond this radius of convergence.