SpecFunc_LambertW

SpecFunc_LambertW(x, principal=True)

Lambert W function.

The Lambert W function \mathrm{W}(x) is defined by the relation:

x = \mathrm{W}(x) \exp(\mathrm{W}(x))

Parameters:

x : float

principal : bool, optional

By default, principal is True.

Returns:

result : float

  • If principal is True : result = \mathrm{W}_0(x). \mathrm{W}_0(x) is referred to as the principal branch of the Lambert W function. It denotes the upper part of the function whose domain is [-1/e, +\infty[ and range [-1, +\infty[.
  • If principal is False : result = \mathrm{W}_{-1}(x). \mathrm{W}_{-1}(x) is the second real branch of the Lambert W function. It denotes the lower part of the function whose domain is [-1/e, 0[ and range ]-\infty, -1].