Spence's function
In mathematics, Spence's function, or dilogarithm, denoted as Li2(z), 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 (the integral definition constitutes its analytical extension to the complex plane): Alternatively, the dilogarithm function is sometimes defined as In hyperbolic geometry the dilogarithm can be used to compute the volume of an . Specifically, a simplex whose vertices have cross ratio z has hyperbolic volume The function D(z) is sometimes called the Bloch-Winger function. Lobachevsky's function and Clausen's function are closely related functions. William Spence, after whom the function was named by early writers in the field, was a Scottish mathematician working in the early nineteenth century. He was at school with John Galt, who later wrote a biographical essay on Spence. (Wikipedia).
