Next: Complex Argument, Up: Dilogarithm [Index]

- Function:
*double***gsl_sf_dilog***(double*`x`) - Function:
*int***gsl_sf_dilog_e***(double*`x`, gsl_sf_result *`result`) These routines compute the dilogarithm for a real argument. In Lewin’s notation this is

*Li_2(x)*, the real part of the dilogarithm of a real*x*. It is defined by the integral representation*Li_2(x) = - \Re \int_0^x ds \log(1-s) / s*. Note that*\Im(Li_2(x)) = 0*for*x <= 1*, and*-\pi\log(x)*for*x > 1*.Note that Abramowitz & Stegun refer to the Spence integral

*S(x)=Li_2(1-x)*as the dilogarithm rather than*Li_2(x)*.