new to Analytica 5.0
Returns the value x that solves
- $ z = x * Exp(x) $.
where Exp is the exponential function.
This is also known as the Lambert W function, often denoted as $ W_0(z) $ in mathematical publications. It appears in the analytic solution of many equations involving exponentials and non-exponentials in the same equation.
The solution is unique when z ≥ 0 or z = -exp(-1). There are two solutions when -exp(-1) < z < 0, in which case ProductLog returns the main branch, whose value is greater than -1. The secondary branch, whose values are less that -1 in the -exp(-1) < z < 0 interval, is not available from this function.
When «z» is a complex number, or z < -exp(-1), the result is a complex number. To obtain the complex result when the parameter is real-valued, you need to set the EnableComplexNumbers system variable to 1.
Introduced in Analytica 5.0.