| @cindex Clausen functions |
| |
| The Clausen function is defined by the following integral, |
| @tex |
| \beforedisplay |
| $$ |
| Cl_2(x) = - \int_0^x dt \log(2 \sin(t/2)) |
| $$ |
| \afterdisplay |
| @end tex |
| @ifinfo |
| |
| @example |
| Cl_2(x) = - \int_0^x dt \log(2 \sin(t/2)) |
| @end example |
| |
| @end ifinfo |
| @noindent |
| It is related to the dilogarithm by |
| @c{$Cl_2(\theta) = \Im(Li_2(e^{i\theta}))$} |
| @math{Cl_2(\theta) = \Im Li_2(\exp(i\theta))}. |
| The Clausen functions are declared in the header file |
| @file{gsl_sf_clausen.h}. |
| |
| @deftypefun double gsl_sf_clausen (double @var{x}) |
| @deftypefunx int gsl_sf_clausen_e (double @var{x}, gsl_sf_result * @var{result}) |
| These routines compute the Clausen integral @math{Cl_2(x)}. |
| @end deftypefun |
