Difference between revisions of "Lerch transcendent"

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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