What is Spence's function?

In mathematics, Spence's function, or dilogarithm, denoted as Li2, is a particular case of the polylogarithm. Two related special functions are referred to as Spence's function, the dilogarithm itself:

and its reflection.For |z| < 1, an infinite series also applies :

Alternatively, the dilogarithm function is sometimes defined as

In hyperbolic geometry the dilogarithm Li2 occurs as the hyperbolic volume of an ideal simplex whose ideal vertices have cross ratio z. Lobachevsky's function and Clausen's function are closely related functions.