Difference between revisions of "Lerch zeta function"
From specialfunctionswiki
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| + | [http://arxiv.org/pdf/1506.06161v1.pdf The Lerch zeta function III. Polylogarithms and special values] | ||
Revision as of 02:29, 23 June 2015
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.
Proof
References
References
The Lerch zeta function III. Polylogarithms and special values
