Difference between revisions of "Lerch transcendent"
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The Lerch transcendent $\Phi$ is defined by | The Lerch transcendent $\Phi$ is defined by | ||
$$\Phi(z,s,a)=\displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{(a+k)^s}.$$ | $$\Phi(z,s,a)=\displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{(a+k)^s}.$$ | ||
| + | |||
| + | =Properties= | ||
| + | {{:Lerch transcendent polylogarithm}} | ||
Revision as of 01:08, 21 March 2015
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.
