taylor series expansion for a rational function

Question

What is the Taylor Series Expansion (function of z ) for

where $\eta$, $n$ and $p$ are positive real constants

Based on the answers in the comments, does this mean that the taylor series is given as

Are there any conditions on the value of ($\eta z$)?

Answer 1

HINT:

Use the binomial series of $(1+\alpha)^{-p}$. The replace each $\alpha$ by $(\eta z)^n$.

The binomial series will start:

$$\frac{1}{(1+\alpha)^p} = 1 -p\alpha + \frac{p(p+1)}{2!}\alpha^2 - \frac{p(p+1)(p+2)}{3!}\alpha^3+\cdots $$