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Super root is an invertion of tetration. Lets define $f(x) = \sqrt[x]{x}_s$. Definition makes sense when x is integer. Is there an extension of this function to real numbers? Similar how Gamma function extends factorial.

greymoose
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    if I'm not mistaken, though extensions of tetrations have been proposed, there isn't one that's conventionally, widely accepted. Thus I suppose that extensions of the super roots exist, but that none is conventionally defined. – Hippalectryon Jul 01 '15 at 09:57
  • If something useful should exist, it's rather the (analoguous) pentation-"squareroot". Unfortunately the pentation is not remotely so far developed as the tetration. Maybe you find something in the "tetration-forum" http://math.eretrandre.org/tetrationforum – Gottfried Helms Jul 01 '15 at 11:54
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    What do you want to know that you can't find on Wikipedia? – wlad Jul 01 '15 at 16:24

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