Polylogarithm

From specialfunctionswiki
Jump to: navigation, search

The polylogarithm $\mathrm{Li}_s$ is defined by the formula for $|z|<1$ by $$\mathrm{Li}_s(z) = \sum_{k=1}^{\infty} \dfrac{z^k}{k^s} = z + \dfrac{z^2}{2^s} + \dfrac{z^3}{3^s} + \ldots$$ A special case of the polylogarithm with $s=2$ is called a dilogarithm.

Properties[edit]

Lerch transcendent polylogarithm
Legendre chi in terms of polylogarithm

Videos[edit]

polylogarithm function

References[edit]

Logarithm and friends