1

is it possible to find a value for this operation: ${^{(3/2)}2}$? If so, can we generalize the domain of the function ${^{x}a}$ to the real or even complex numbers?

I had originally tried to solve the proposed operation by finding $ssrt({^{3}2})$ and $^{3}({ssrt(2)})$, however, the results are different.

Thanks for your help :)

Juan Diego Parales Somogyi
  • 29
  • 4
    Simply googling tetration will lead you to a lot of writing on this topic, although because the tetration operation does not behave very well in ways that would allow reasonably straightforward results for something like this, the actual generalizations spread out into several distinct possible approaches, with none of them really all that satisfactory or seemingly dominate over the others as the most reasonable generalization. – Dave L. Renfro Mar 02 '22 at 06:53
  • I, for one, disagree with the close vote. I don't see what context is missing, or what kind of additional context could be provided that would make this question easier to answer than it already is (indeed, @DaveL.Renfro's comment can already be extended.to a perfectly viable answer). – Z. A. K. Mar 02 '22 at 08:01
  • @Z. A. K.: I didn't vote to close, and don't have time to attempt an informative answer, but I also suspect this is likely a duplicate of at least two or three other questions that can be found in MSE under the tetration tag or by a straightforward search in mathoverflow. – Dave L. Renfro Mar 02 '22 at 09:38
  • @DaveL.Renfro: I'm in a similar situation, and I agree that it's almost certainly a duplicate. And if so, it should be closed for being a duplicate, not for missing context. – Z. A. K. Mar 02 '22 at 09:48
  • Some more informative answers exists at this (more informative) question: https://math.stackexchange.com/questions/3007951/tetration-by-a-non-integer . Perhaps this question should be closed to not duplicate (or multiplicate) conversation? (didn't vote so far) – Gottfried Helms Mar 03 '22 at 16:47
  • Thanks for the link to that question, and If it is the best @GottfriedHelms to close my question, how can I do it? – Juan Diego Parales Somogyi Mar 04 '22 at 01:28
  • Juan DPS - this can be done, if some (I think 5) users of high-enough reputation "vote-to-close". There has so far been 1 "vote-to-close", I can do the next vote, if you're fine with it. (I'll do it tomorrow, I'm just leaving for night...) – Gottfried Helms Mar 04 '22 at 01:38
  • It's ok @GottfriedHelms – Juan Diego Parales Somogyi Mar 06 '22 at 03:10

0 Answers0