Dilogarithm Function/Examples

Examples of Dilogarithm Function

Example: $\map {\Li_2} {-\phi}$

$\map {\Li_2} {-\phi} = -\dfrac 3 5 \map \zeta 2 - \paren {\map \ln \phi}^2$

Example: $\map {\Li_2} {-1}$

$\map {\Li_2} {-1} = -\dfrac 1 2 \map \zeta 2$

Example: $\map {\Li_2} {-\dfrac 1 \phi}$

$\map {\Li_2} {-\dfrac 1 \phi} = -\dfrac 2 5 \map \zeta 2 + \dfrac 1 2 \paren {\map \ln \phi}^2$

Example: $\map {\Li_2} 0$

$\map {\Li_2} 0 = 0$

Example: $\map {\Li_2} {1 - \dfrac 1 \phi}$

$\map {\Li_2} {1 - \dfrac 1 \phi} = \dfrac 2 5 \map \zeta 2 - \paren {\map \ln \phi}^2$

Example: $\map {\Li_2} {\dfrac 1 2 }$

$\map {\Li_2} {\dfrac 1 2} = \dfrac 1 2 \paren {\map \zeta 2 - \paren {\map \ln 2}^2}$

Example: $\map {\Li_2} {\dfrac 1 \phi}$

$\map {\Li_2} {\dfrac 1 \phi} = \dfrac 3 5 \map \zeta 2 - \paren {\map \ln \phi}^2$

Example: $\map {\Li_2} 1$

$\map {\Li_2} 1 = \map \zeta 2$