# Power series over integral change of variables

Let $y$ be given by $$y=\int_x^\infty \frac{dx'}{(1+x'^2)^\alpha}$$ where $\alpha>1$. Is it possible to express the following as a series: $$x(1+x^2)^{\alpha-1}=\sum a_n\left(\frac{1}{y}\right)^n$$

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