Superroots and a generalization for the Lambert-W

[Gottfried]

I believe I may have found a closed form for the third superroot / generalized LambertW function:
\(
{}^{3}W(v) = \log\left(\sqrt[3]{e^v}_s\right) = \sum_{k=0}^{\infty}
\frac{v^k}{k!} \sum_{j=0}^k
{k-1 \choose j}j(k-j)^{j-2}(-k)^{k-j}
\)

Regards,
Andrew Robbins

Hah, that sounds good, I'll try it tomorrow! (I've just seen formulae 96-100 in your earlier announced paper, but can read it also not before tomorrow afternoon) Did you see already whether it is possibly simply extensible to higher orders?

Gottfried