>>12545417polylogarithms
In Don Zagier's words:
>the dilogarithm is one of the simplest non-elementary functions onecan imagine. It is also one of the strangest. It occurs not quite often enough,
and in not quite an important enough way, to be included in the Valhalla of
the great transcendental functions—the gamma function, Bessel and Legendre
- functions, hypergeometric series, or Riemann’s zeta function. And yet
it occurs too often, and in far too varied contexts, to be dismissed as a mere
curiosity. First defined by Euler, it has been studied by some of the great
mathematicians of the past—Abel, Lobachevsky, Kummer, and Ramanujan,
to name just a few—and there is a whole book devoted to it. Almost all
of its appearances in mathematics, and almost all the formulas relating to it,
have something of the fantastical in them, as if this function alone among all
others possessed a sense of humor
Polylogarithm ladders are one of the coolest functional relations in all of mathematics
