Compute the Lambert W functions for the numbers converted to symbolic objects.
For most symbolic (exact) numbers, lambertw returns unresolved
symbolic calls.
Plot the two main branches, and , of the Lambert W function.
syms x
fplot(lambertw(x))
hold on
fplot(lambertw(-1,x))
hold off
axis([-0.5 4 -4 2])
title('Lambert W function, two main branches')
legend('k=0','k=1','Location','best')
x — Input number | vector | matrix | array | symbolic number | symbolic variable | symbolic array | symbolic function | symbolic expression
Input, specified as a number, vector, matrix, or array, or a
symbolic number, variable, array, function, or expression.
At least one input argument must be a scalar, or both arguments must be vectors
or matrices of the same size. If one input argument is a scalar and the other is a
vector or matrix, lambertw expands the scalar into a vector or
matrix of the same size as the other argument with all elements equal to that
scalar.
k — Branch of Lambert W function integer | vector or matrix of integers | symbolic integer | symbolic vector or matrix of integers
Branch of Lambert W function, specified as an integer, a vector or matrix of integers, a
symbolic integer, or a symbolic vector or matrix of integers.
At least one input argument must be a scalar, or both arguments must be vectors
or matrices of the same size. If one input argument is a scalar and the other is a
vector or matrix, lambertw expands the scalar into a vector or
matrix of the same size as the other argument with all elements equal to that
scalar.
The Lambert W function W(x) represents
the solutions y of the equation for any complex number x.
For complex x, the equation has
an infinite number of solutions y = lambertW(k,x) where k ranges
over all integers.
For all real x ≥ 0, the equation has exactly one real solution y = lambertW(x) =
lambertW(0,x).
For real x where , the equation has exactly two real solutions. The larger
solution is represented by y = lambertW(x) and the smaller solution by y = lambertW(–1,x).
For , the equation has exactly one real solution y = –1 = lambertW(0, –exp(–1)) = lambertW(–1,
-exp(–1)).
References
[1] Corless, R.M., G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey, and D.E. Knuth. "On the Lambert
W Function." Advances in Computational Mathematics, Vol. 5, pp.
329–359, 1996.
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.