# How to compute inner product in the Hardy space

1. Sep 29, 2012

### LikeMath

Hi,
Let $H^2$ be the Hardy space on the open unit disk.
I am wondering how can I compute the following inner product

$<\frac{1}{\left(1-\overline{\alpha_1} z\right)^2}\frac{z-\alpha_2}{1-\overline{\alpha_2} z},\frac{z}{\left(1-\overline{\alpha_1} z\right)^2}>,$

where $\alpha_1,\alpha_2$ in the unit disk.

I tried to expand the functions but it became complicated. Also it did not work with the integration.

Is there an idea to be tried?