Formula:8417

Digital Library of Mathematical Functions ID 25.12.E5

${\displaystyle{\displaystyle\mathrm{Li}_{2}\left(z^{m}\right)=m\sum_{k=0}^{m-1}\mathrm{Li}_{2}\left(ze^{2\pi ik/m}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle|z|<1}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{Li}_{2}\left(\NVar{z}\right)}}$: dilogarithm
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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