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## Re: [newbie] unexpected behaviour for x^x

 From: Julien Bect Subject: Re: [newbie] unexpected behaviour for x^x Date: Fri, 12 Dec 2014 18:22:05 +0100 User-agent: Mozilla/5.0 (X11; Linux i686; rv:31.0) Gecko/20100101 Thunderbird/31.3.0

```Le 12/12/2014 17:56, Jean Dubois a écrit :
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However for x real: lim_{x-->0-} x^x is non-existing, even though numerically calculating lim_{x-->0-} x^x might suggest you get a complex number
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What do you mean by "non-existing" ? "might suggest" ?

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The logarithm of a complex number is perfectly well-defined, and it *is* a complex number.
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Actually, the complex log is a multi-valued function, so the "well-defined" log I'm talking about is the principal value; see, e.g.,
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https://en.wikipedia.org/wiki/Complex_logarithm

To sum up:

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1) x^x = exp (x * log (x)) is a perfectly well defined complex number, even for negative x, as soon as a branch of the complex log has been singled out
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2) Octave computes the principal value of the log, i.e., log(z) is the only logarithm of z that has its imaginary part in (pi; pi].
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