GNU Scientific Library Reference Manual - Third Edition (v1.12)by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi Paperback (6"x9"), 592 pages, 60 figures ISBN 0954612078 RRP £24.95 ($39.95) |

## 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).

ISBN 0954612078 | GNU Scientific Library Reference Manual - Third Edition (v1.12) | See the print edition |