Series expansion and Laurent series

I need to find the series expansion at $$z=0$$ and the Laurent series at $$\sqrt{ 2/3} <|z| < \infty$$ for the function $$f(z)= \frac{1}{(2-3z^{2})^2}$$ I guess I first need to first find the partial fraction decomposition

• It seems like you already know what you need to do. Maybe try computing the partial fraction decomposition and edit your question if you are still unsure of how to proceed. Jan 12 at 16:43

Hint: $$\;f(z)=\dfrac{\left(\dfrac12\right)^2}{\left(1-\dfrac32z^2\right)^2}=\dfrac {\left(\dfrac1{3z^2}\right)^2}{\left(1-\dfrac2{3z^2}\right)^2}\;$$ and $$\;\dfrac 1{(1-x)^2}=1+2x+3x^2+\cdots$$