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How do we compute higher order derivatives of a rational function?
Let $a \in (-1,1)$ and $x\in {\mathbb R}$ and consider a following sequence of rational functions:
\begin{eqnarray}
R^{(0)}[x]&:=& \frac{x (a x-1)}{a x-x^2+x-1}\\
R^{(1)}[x]&:=& -\frac{...
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