Find a series

[Солунац]

Let $f(z)=\frac 1 \sqrt {z^2-1}$, but for $\sqrt{ z^2-1}$ is chosen a branch (regular) wich is positive for $|z|>1$. Find a series of function $f(z)$ in a neighborhood of $a=\infty$ and determine radius convergence for that series.

С НОВЫМ ГОДОМ!

[ewert]

$$f(z)={1\over z}\left(1-{1\over z^2}\right)^{-1/2}\;;$$

$$(1+w)^{\alpha}=\;?$$

(for small $w$)

[Солунац]

Aaaa, спасибо.