


Lambert W Functions
===================

Lambert's :math:`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
:math:`W_{-1}(x)` to be the other real branch, where :math:`W < -1` for :math:`x < 0`.

.. index:: Lambert W function

.. function:: gsl_sf_lambert_W0(x)

 This routine computes the principal branch of the Lambert :math:`W` function,
 :math:`W_0(x)`.

.. function:: gsl_sf_lambert_Wm1(x)

 This routine computes the secondary real-valued branch of the Lambert
 :math:`W` function, :math:`W_{-1}(x)`.
