LambertW

LambertW (z, branch)

The LambertW function returns the complex value of Lambert's W function for complex z and integer index branch. The function can be defined through its inverse,

$$\displaystyle z=w \mathrm{e}^{w} .$$

Since w is multivalued, the branch parameter is used to differentiate between solutions for the equation.

The LambertW function was added in Igor Pro 7.00.

Details

IGOR's LambertW uses complex input and output. You can use LambertW in real expressions but you must make sure that you are not calling the function in a range where its imaginary part is non-zero.

The average accuracy of the function defined by:

cabs(z-w*exp(w))

in the region

|real(z)| < 10, |imag(z)| < 10

is 5e-14. In general the accuracy decreases with increasing |branch| and with increasing distance from the origin in the z-plane.

IGOR uses a hybrid algorithm to compute the function which requires longer computation times in the presence of numerical instabilities.

References

R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey and D.E. Knuth, "On Lambert W Function", Advances in Computational Mathematics 5: 329–359