Is $\displaystyle x^x$ an elementary function?

I do not think it is, is that right?

Printable View

- Jan 19th 2006, 01:08 PMThePerfectHackerIs this elementary.
Is $\displaystyle x^x$ an elementary function?

I do not think it is, is that right? - Jan 19th 2006, 04:44 PMJameson
I think it is elementary. The integral however isn't. Check out MathWorld's page on elementary functions for a definition.

http://mathworld.wolfram.com/ElementaryFunction.html - Jan 19th 2006, 05:36 PMhpeQuote:

Originally Posted by**ThePerfectHacker**

- Jan 19th 2006, 06:00 PMThePerfectHacker
Curious, why is $\displaystyle \int e^{x^2}dx$ not elementary? How do you prove it?

It seems to be anagolus with Galios' Theory for the insolvability of the quintic. Namely, to show that in finite steps a solution cannot be reached.