I am considering the following complex potential for a fluid flow
$w = U a \bigg(\frac{z}{a} \bigg)^{\pi/ \alpha}$.
I would like to obtain the velocity potential and stream function from this: one could do this by writing out $z = r e^{i \theta}$ and then expanding out the power. However, what does one do in the situation that the power is not an integer, as now the power is a fraction of $\pi$, which is irrational.