Li 2(z)+Li 2(1-z)=pi^2/6-log(z)log(1-z)

Theorem

The following formula holds: $$\mathrm{Li}_2(z)+\mathrm{Li}_2(1-z)=\dfrac{\pi^2}{6} - \log(z)\log(1-z),$$ where $\mathrm{Li}_2$ denotes the dilogarithm, $\pi$ denotes pi, and $\log$ denotes the logarithm.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $27.7.3$ (note: the letter $f$ denotes the dilogarithm in this formula)