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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