Formula:DLMF:25.14:E3

<< Formula:DLMF:25.14:E2

formula in Lerch's Transcendent

Lerch's Transcendent >>

${\displaystyle{\displaystyle{\displaystyle\Polylogarithm{s}@{z}=z\Phi\left(z,s,1\right)}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\Re{s}>1}}}$ &
${\displaystyle{\displaystyle{\displaystyle|z|\leq 1}}}$

Proof

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Symbols List

& : logical and
${\displaystyle{\displaystyle{\displaystyle\mathrm{Li}_{s}}}}$ : polylogarithm : http://dlmf.nist.gov/25.12#E10
${\displaystyle{\displaystyle{\displaystyle\Phi}}}$ : Lerch's transcendent : http://dlmf.nist.gov/25.14#E1
${\displaystyle{\displaystyle{\displaystyle\Re{z}}}}$ : real part : http://dlmf.nist.gov/1.9#E2

Bibliography

Equation (3), Section 25.14 of DLMF.

URL links

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<< Formula:DLMF:25.14:E2

formula in Lerch's Transcendent

Lerch's Transcendent >>