The following is called a J continued fraction:

$$\cfrac{\alpha_0}{1+a_0x-\cfrac{b_1x^2}{1+a_1x-\cfrac{b_2x^2}{1+a_2x-\cdots}}}$$

where the constants are real numbers. Let $\alpha_n= \frac{1}{(n+1)^2}$ for $n\geq 0$. I want to write the J-fraction expansion of the power series $\sum_{n=0}^\infty \alpha_nx^n.$ Is there any algorithm for this? If not, what should be a good start?

`Series`

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