Non integer Hyper-powers.

Asked Dec 26 '19 at 03:19

Active Dec 26 '19 at 03:27

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If I have a function $y=x^x$, that can be denoted in hyperpower notation as $^2x$, but I will be denoting it as $ y= $ hyp$_2(x) $. In general, for hyperpowers, $y=x^{x^{x^{...}x}}$ or in my notation $ y= $ hyp$_\alpha(x) $. The problem with the hyperpowers I don't know how to calculate them for non-integer $\alpha$. Is it even possible to have non-integer $\alpha$?

Thanks.

edited Dec 26 '19 at 03:27

Simply Beautiful Art

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asked Dec 26 '19 at 03:19

Joshua Pasa

https://www.tandfonline.com/doi/abs/10.1080/10652460500422247?journalCode=gitr20 – Barry Smith Dec 26 '19 at 03:24
See also: [How to evaluate fractional tetrations?](https://math.stackexchange.com/questions/238970/how-to-evaluate-fractional-tetrations) – Simply Beautiful Art Dec 26 '19 at 03:30

Non integer Hyper-powers.

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