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:

$$

operatorname{Li}_2(z) = -int_0^z{ln|1-zeta| over zeta}, mathrm{d}zeta = sum_{k=1}^infty {z^k over k^2};

• the dilogarithm with its argument multiplied by −1:

$$

F(z)=operatorname{Li}_2(-z) = int_0^z{ln(1+zeta) over zeta}, mathrm{d}zeta = sum_{k=1}^infty {(-z)^k over k^2}.

Here the series can only be used for |z| < 1, inside its radius of convergence.

A computer routine to compute the dilogarithm using approximation by truncated Chebyshev series is available, for example, as TMath::DiLog() in the open-source ROOT data analysis package.