Formula:DLMF:25.12:E6

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formula in Polylogarithms

Formula:DLMF:25.12:E7 >>

${\displaystyle{\displaystyle{\displaystyle\Dilogarithm@{x}+\Dilogarithm@{1-x}=\frac{1}{6}{\pi^{2}}-(\ln x)\ln\left(1-x\right)}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle 0<x<1}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{Li}_{2}}}}$ : dilogarithm : http://dlmf.nist.gov/25.12#E1
${\displaystyle{\displaystyle{\displaystyle\pi}}}$ : ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
${\displaystyle{\displaystyle{\displaystyle\mathrm{ln}}}}$ : principal branch of logarithm function : http://dlmf.nist.gov/4.2#E2

Bibliography

Equation (6), Section 25.12 of DLMF.

URL links

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