Abel's Functional Equation

Let $\mathop{\rm Li}\nolimits _2(x)$ denote the Dilogarithm, defined by

$\begin{displaymath} \mathop{\rm Li}\nolimits _2(x)=\sum_{n=1}^\infty {x^n\over n^2}, \end{displaymath}$

then

$\begin{displaymath} \mathop{\rm Li}\nolimits _2(x)+\mathop{\rm Li}\nolimits _2(y... ...eft({y(1-x)\over 1-xy}\right)=3\mathop{\rm Li}\nolimits _2(1). \end{displaymath}$

See also Dilogarithm, Polylogarithm, Riemann Zeta Function