Formula:DLMF:25.12:E16:SE1

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F s ⁢ ( x ) = - \Polylogarithm ⁢ s + 1 ⁢ @ - e x subscript 𝐹 𝑠 𝑥 \Polylogarithm 𝑠 1 @ 𝑥 {\displaystyle{\displaystyle{\displaystyle F_{s}(x)=-\Polylogarithm{s+1}@{-{% \mathrm{e}^{x}}}}}}

Proof

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Symbols List

Li s subscript Li 𝑠 {\displaystyle{\displaystyle{\displaystyle\mathrm{Li}_{s}}}}  : polylogarithm : http://dlmf.nist.gov/25.12#E10
e e {\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}  : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11

Bibliography

Equation (16), Section 25.12 of DLMF.

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