Two fun W (Lambert function) facts: 1) The Taylor series of W records the number of spanning trees of the complete graphs. 2) If 1/2+i y_n is the nth zero of the Riemann zeta function on the critical line, then asymptotically (large n) y_n ~ 2 pi (n-11/8)/ W((n-11/8)/e) -Veit

On Jun 2, 2016, at 10:28 PM, Dan Asimov <dasimov@earthlink.net> wrote:

Thanks. I vastly prefer the Lambert W function when it is not defined with a branch cut but is allowed to extend to it full Lambertness on a Riemann surface.

Whether considering the Lambert function or the more simply defined function of which it is the inverse function:

f(z) = z exp(z),

the aforesaid Riemann surface is just the subset of C^2 defined as

{(z,w) | z = w exp(w)}.

This is, in my opinion, the appropriate object of study.

—Dan