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