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2 votes

$n$th root of $(a,b) \mapsto (\operatorname{gm}, \operatorname{am})$

A simple scheme (a parallel of which can be used to define the Gamma function from the factorial) is as follows: call $T$ your function, then define the functional square root as $$T^{\frac{1}{2}}=\l …
Yaakov Baruch's user avatar