| @cindex W function |
| @cindex Lambert function |
| |
| Lambert's W functions, @math{W(x)}, are defined to be solutions |
| of the equation @math{W(x) \exp(W(x)) = x}. This function has |
| multiple branches for @math{x < 0}; however, it has only |
| two real-valued branches. We define @math{W_0(x)} to be the |
| principal branch, where @math{W > -1} for @math{x < 0}, and |
| @c{$W_{-1}(x)$} |
| @math{W_@{-1@}(x)} to be the other real branch, where |
| @math{W < -1} for @math{x < 0}. The Lambert functions are |
| declared in the header file @file{gsl_sf_lambert.h}. |
| |
| |
| @deftypefun double gsl_sf_lambert_W0 (double @var{x}) |
| @deftypefunx int gsl_sf_lambert_W0_e (double @var{x}, gsl_sf_result * @var{result}) |
| These compute the principal branch of the Lambert W function, @math{W_0(x)}. |
| @comment exceptions: GSL_EDOM, GSL_EMAXITER |
| @end deftypefun |
| |
| @deftypefun double gsl_sf_lambert_Wm1 (double @var{x}) |
| @deftypefunx int gsl_sf_lambert_Wm1_e (double @var{x}, gsl_sf_result * @var{result}) |
| These compute the secondary real-valued branch of the Lambert W function, |
| @c{$W_{-1}(x)$} |
| @math{W_@{-1@}(x)}. |
| @comment exceptions: GSL_EDOM, GSL_EMAXITER |
| @end deftypefun |
| |
