Lerch transcendent
From specialfunctionswiki
The Lerch transcendent $\Phi$ is defined by $$\Phi(z,s,a)=\displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{(a+k)^s}.$$
Contents
Properties
Theorem
The following formula holds: $$\Phi(z,n,1)=\dfrac{\mathrm{Li}_n(z)}{z},$$ where $\Phi$ denotes the Lerch transcendent and $\mathrm{Li_n}$ denotes the polylogarithm.
