Expressions involving polylog are combined as follows

where n is an integer greater than one, b is real, a, w, x, y, and z are variables assumed to be complex, where $1\le \left|x\right|$, and $\left|y\right|<1$.

$\mathrm{combine}\left(\mathrm{polylog}\left(a\&comma;x\right)+\mathrm{polylog}\left(a\&comma;-x\right)\&comma;\mathrm{polylog}\right)$

$2^{1-a}\mathrm{polylog}\left(a\&comma;x^2\right)$

$\mathrm{assume}\left(1<x\right)$

$\mathrm{combine}\left(\mathrm{polylog}\left(2\&comma;x\right)+\mathrm{polylog}\left(2\&comma;\frac{x}{x-1}\right)\&comma;\mathrm{polylog}\right)$

$\frac{{\mathrm{\pi }}^2}{2}-2\mathrm{I}\mathrm{\pi }\ln \left(\mathrm{x~}\right)+\mathrm{I}\mathrm{\pi }\ln \left(\mathrm{x~}-1\right)-\frac{{\ln \left(\mathrm{x~}-1\right)}^2}{2}$

$\mathrm{assume}\left(x\&comma;\mathrm{RealRange}\left(-1\&comma;1\right)\right)$

$\mathrm{combine}\left(\mathrm{polylog}\left(4\&comma;x\right)+\mathrm{polylog}\left(4\&comma;\frac{1}{x}\right)\&comma;\mathrm{polylog}\right)$

$-\frac{{\ln \left(-\frac{1}{\mathrm{x~}}\right)}^2{\mathrm{\pi }}^2}{12}-\frac{7{\mathrm{\pi }}^4}{360}-\frac{{\ln \left(-\frac{1}{\mathrm{x~}}\right)}^4}{24}$

$\mathrm{assume}\left(x<1\right)$

$\mathrm{combine}\left(\mathrm{polylog}\left(3\&comma;x\right)+\mathrm{polylog}\left(3\&comma;1-x\right)+\mathrm{polylog}\left(3\&comma;\frac{x}{x-1}\right)\&comma;\mathrm{polylog}\right)$

$\mathrm{\zeta }\left(3\right)+\frac{{\mathrm{\pi }}^2\ln \left(1-\mathrm{x~}\right)}{6}-\frac{\ln \left(\mathrm{x~}\right){\ln \left(1-\mathrm{x~}\right)}^2}{2}+\frac{{\ln \left(1-\mathrm{x~}\right)}^3}{6}$

$\mathrm{combine}\left(\mathrm{polylog}\left(3\&comma;\exp \left(\mathrm{I}\right)\right)-\mathrm{polylog}\left(3\&comma;\exp \left(-\mathrm{I}\right)\right)\&comma;\mathrm{polylog}\right)$

$\frac{\mathrm{I}{\mathrm{\pi }}^2}{3}+\frac{\mathrm{I}}{6}-\frac{\mathrm{I}\mathrm{\pi }}{2}$