Re: [newbie] unexpected behaviour for x^x

[Julien Bect]

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" ?

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].