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 realvalued 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 \(x < 0\).

gsl_sf_lambert_W0
(x)¶ This routine computes the principal branch of the Lambert \(W\) function, \(W_0(x)\).

gsl_sf_lambert_Wm1
(x)¶ This routine computes the secondary realvalued branch of the Lambert \(W\) function, \(W_{1}(x)\).