12/25/2015, 06:16 AM
Conjecture:
Let \( \sqrt[3]{w}_s^{(z)} = x \) iff. \( \exp_x^3(z) = w \), then:
\(
\sqrt[3]{w}_s^{(z)} = \exp \left( \sum_{k=0}^{\infty}
\frac{\log(w)^k}{k!} \sum_{j=0}^{k-1} {k-1 \choose j}(k-j-1)^j(-k)^{k-j-1} z^j \right)
\)
Discussion:
How and why?
For more discussion see this thread
Let \( \sqrt[3]{w}_s^{(z)} = x \) iff. \( \exp_x^3(z) = w \), then:
\(
\sqrt[3]{w}_s^{(z)} = \exp \left( \sum_{k=0}^{\infty}
\frac{\log(w)^k}{k!} \sum_{j=0}^{k-1} {k-1 \choose j}(k-j-1)^j(-k)^{k-j-1} z^j \right)
\)
Discussion:
How and why?
For more discussion see this thread