11/24/2015, 12:51 AM
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
\(
{}^{3}W(v) = \log\left(\sqrt[3]{e^v}_s\right) = \sum_{k=0}^{\infty}
\frac{v^k}{k!} \sum_{j=0}^k
{k-1 \choose j}j(k-j)^{j-2}(-k)^{k-j}
\)
Regards,
Andrew Robbins