Formula:8423

Digital Library of Mathematical Functions ID 25.12.E11

${\displaystyle{\displaystyle\mathrm{Li}_{s}\left(z\right)\equiv\frac{z}{\Gamma\left(s\right)}\int_{0}^{\infty}\frac{x^{s-1}}{e^{x}-z}\mathrm{d}x,}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\equiv}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\mathrm{Li}_{\NVar{s}}\left(\NVar{z}\right)}}$: polylogarithm
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle s}}$: complex variable
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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