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Furthermore, $H(x)=\sum_{m=0}^\infty F_{m,m}x^m$ is the constant term of $G(x/y,y)$, and can be found via residue calculus as \begin{align*} H(x)&=\frac{1}{2\pi i}\int_\gamma\frac{1}{y}G(x/y,y)\,dy\\ &=\frac{1}{2\pi i}\int_\gamma\frac{1}{y}R(x/y,y)\,dy\\ &=\sum_k\mathrm{Res}\left[\frac{1}{y}R(x/y,y),y=z_k\right] \end{align*} where $\gamma$ is a ...
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