Difference between revisions of "Lerch transcendent"
From specialfunctionswiki
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[[Dirichlet beta in terms of Lerch transcendent]]<br /> | [[Dirichlet beta in terms of Lerch transcendent]]<br /> | ||
[[Legendre chi in terms of Lerch transcendent]]<br /> | [[Legendre chi in terms of Lerch transcendent]]<br /> | ||
| + | [[Li2(z)=zPhi(z,2,1)]]<br /> | ||
=References= | =References= | ||
Revision as of 03:03, 25 June 2017
The Lerch transcendent $\Phi$ is defined for $|z|<1$ and $a \in \mathbb{C} \setminus \{ 0,-1,-2,\ldots\}$ by $$\Phi(z,s,a)=\displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{(a+k)^s}.$$
Properties
Lerch transcendent polylogarithm
Relationship between Lerch transcendent and Lerch zeta
Dirichlet beta in terms of Lerch transcendent
Legendre chi in terms of Lerch transcendent
Li2(z)=zPhi(z,2,1)
References
- 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.11 (1)$
