## File: Lambert-W-Functions.html

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 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103` `````` GNU Scientific Library – Reference Manual: Lambert W Functions

7.23 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)
Function: int gsl_sf_lambert_W0_e (double x, gsl_sf_result * result)

These compute the principal branch of the Lambert W function, W_0(x).

Function: double gsl_sf_lambert_Wm1 (double x)
Function: int gsl_sf_lambert_Wm1_e (double x, gsl_sf_result * result)

These compute the secondary real-valued branch of the Lambert W function, W_{-1}(x).

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