03/03/2019, 07:29 AM
(This post was last modified: 03/03/2019, 07:31 AM by Micah.
Edit Reason: found source of interest
)
Are we certain that the form posted on Wikipedia is correctly derived? Without the proof there may be no way of knowing it's correctness, We could take a look at the first few cases of the integral in order to inspect the forms, and then conjecture about a generalization from there, have you derived the first few forms of the integral?
\( \int\limits x^x dx = I_1 \)
\( \int\limits x^{x^x} dx = I _2 \)
\( \dots \)
That may be a starting point for a proof. Also, I may be misinterpreting something on the wikipedia page that you posted, but shouldn't there be constants of integration in all of these antiderivatives as they do not have limits?
This may also be of some use: https://en.wikipedia.org/wiki/Puiseux_series
Thanks for the thought provoking question!
-Micah
\( \int\limits x^x dx = I_1 \)
\( \int\limits x^{x^x} dx = I _2 \)
\( \dots \)
That may be a starting point for a proof. Also, I may be misinterpreting something on the wikipedia page that you posted, but shouldn't there be constants of integration in all of these antiderivatives as they do not have limits?
This may also be of some use: https://en.wikipedia.org/wiki/Puiseux_series
Thanks for the thought provoking question!
-Micah
