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.
