lambertw (Symbolic Math Toolbox)

Lambert's W function

Syntax

```
Y = lambertw(X)
```

Description

lambertw(X) evaluates Lambert's W function at the elements of X, a numeric matrix or a symbolic matrix. Lambert's W solves the equation

for w as a function of x.

Examples

lambertw([0 -exp(-1); pi 1]) returns

         0   -1.0000 
    1.0737    0.5671

The statements

```
syms x y
lambertw([0 x;1 y])
```

return

[           0, lambertw(x)]
[ lambertw(1), lambertw(y)]

References

[1] Corless, R.M, Gonnet, G.H., Hare, D.E.G., and Jeffrey, D.J., Lambert's W Function in Maple, Technical Report, Dept. of Applied Math., Univ. of Western Ontario, London, Ontario, Canada.

[2] Corless, R.M, Gonnet, G.H., Hare, D.E.G., and Jeffrey, D.J., On Lambert's W Function, Technical Report, Dept. of Applied Math., Univ. of Western Ontario, London, Ontario, Canada.

Both papers are available by anonymous FTP from

```
cs-archive.uwaterloo.ca
```

jordan laplace