Lerch zeta function

The Lerch zeta function is defined by $$L(\lambda,\alpha,z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{e^{2i \pi \lambda k}}{(n+\alpha)^z}.$$

Properties

Theorem

The following formula holds: $$\Phi(e^{2\pi i \lambda},z,a)=L(\lambda,a,z),$$ where $\Phi$ denotes the Lerch transcendent and $L$ denotes the Lerch zeta function.

References

The Lerch zeta function III. Polylogarithms and special values