Symbolic Math Toolbox™

lambertw - Lambert's W function

Syntax

W = lambertw(X)
W = lambertw(K,X)

Description

W = 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

we^w = x

for w as a function of x.

W = lambertw(K,X) is the K-th branch of this multi-valued function.

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, G.H. Gonnet, D.E.G. Hare, and D.J. Jeffrey, 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. Gonnet, D.E.G. Hare, and D.J. Jeffrey, 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

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