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YCor
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Extension of hyperderivatives

Let $a$ be algebraic over $K:=\mathbb F_q\left(\!\left(\frac1T\right)\!\right)$. Can one extend continuously the hyperderivatives on $K(a)$?

Recal that the hyperderivative $D_h$ over $K$ is defined by $$D_h\left(\sum_{i\le m}\frac{a_i}{T^i}\right)=\sum_{i\le m}\binom{-i}h\frac{a_i}{T^{i+h}}$$ with $\binom{-i}h=\frac{-i(-i-1)\cdots(-i+h-1)}{h!}$

joaopa
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