| @cindex dilogarithm |
| |
| The functions described in this section are declared in the header file |
| @file{gsl_sf_dilog.h}. |
| |
| @menu |
| * Real Argument:: |
| * Complex Argument:: |
| @end menu |
| |
| @node Real Argument |
| @subsection Real Argument |
| |
| @deftypefun double gsl_sf_dilog (double @var{x}) |
| @deftypefunx int gsl_sf_dilog_e (double @var{x}, gsl_sf_result * @var{result}) |
| These routines compute the dilogarithm for a real argument. In Lewin's |
| notation this is @math{Li_2(x)}, the real part of the dilogarithm of a |
| real @math{x}. It is defined by the integral representation |
| @math{Li_2(x) = - \Re \int_0^x ds \log(1-s) / s}. |
| Note that @math{\Im(Li_2(x)) = 0} for @c{$x \le 1$} |
| @math{x <= 1}, and @math{-\pi\log(x)} for @math{x > 1}. |
| |
| @end deftypefun |
| |
| @node Complex Argument |
| @subsection Complex Argument |
| |
| |
| @deftypefun int gsl_sf_complex_dilog_e (double @var{r}, double @var{theta}, gsl_sf_result * @var{result_re}, gsl_sf_result * @var{result_im}) |
| This function computes the full complex-valued dilogarithm for the |
| complex argument @math{z = r \exp(i \theta)}. The real and imaginary |
| parts of the result are returned in @var{result_re}, @var{result_im}. |
| @end deftypefun |
