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Let [itex]H^2[/itex] be the Hardy space on the open unit disk.

I am wondering how can I compute the following inner product

[itex]<\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}>,[/itex]

where [itex]\alpha_1,\alpha_2[/itex] 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?

Thanks in advanced

Likemath