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I know that

$$f{(x)} = a^x$$

is called exponential function and

$$f{(x)} = x^a $$

is the power function.


But what is the name of $f{(x)} = x^x$?

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    $\begingroup$ "Does it matter" function $\endgroup$
    – PleaseHelp
    Nov 11, 2013 at 18:40
  • $\begingroup$ In my class I call it the "base-power" function. Students then onwards know what I am talking about, but I made up that name and it is certainly not an official name. $\endgroup$
    – imranfat
    Nov 11, 2013 at 18:43
  • $\begingroup$ A self powered function. Take that physics. $\endgroup$ Nov 11, 2013 at 19:01
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    $\begingroup$ The act of raising something to its own power is known as tetration, though that might not be what you are looking for. $\endgroup$
    – L. F.
    Nov 11, 2013 at 19:06

1 Answer 1

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As far as I'm aware, it doesn't have a nontrivial one. It is its own name.

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  • $\begingroup$ Moreover, however, it's an instance of tetration. $\endgroup$
    – Shaun
    Feb 18, 2016 at 13:40

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