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

**From**: |
Jean Dubois |

**Subject**: |
Re: [newbie] unexpected behaviour for x^x |

**Date**: |
Fri, 12 Dec 2014 21:25:48 +0100 |

2014-12-12 18:22 GMT+01:00 Julien Bect <address@hidden>:
>* Le 12/12/2014 17:56, Jean Dubois a écrit :*
>*>*
>*> 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*
>
>
>* What do you mean by "non-existing" ? "might suggest" ?*
I added for x real, maybe I should have written "in R: lim_{x-->0-}
x^x is non-existing"
regards,
jean
>
>* The logarithm of a complex number is perfectly well-defined, and it *is* a*
>* complex number.*
>
>* 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.,*
>
>* https://en.wikipedia.org/wiki/Complex_logarithm*
>
>* To sum up:*
>
>* 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*
>
>* 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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