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Diffstat (limited to 'gsl-1.9/doc/specfunc-dilog.texi')
| -rw-r--r-- | gsl-1.9/doc/specfunc-dilog.texi | 33 |
1 files changed, 33 insertions, 0 deletions
diff --git a/gsl-1.9/doc/specfunc-dilog.texi b/gsl-1.9/doc/specfunc-dilog.texi new file mode 100644 index 0000000..696b565 --- /dev/null +++ b/gsl-1.9/doc/specfunc-dilog.texi @@ -0,0 +1,33 @@ +@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 |