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Topic: ln(x^x)
Replies: 22   Last Post: May 10, 2000 5:27 PM

 Messages: [ Previous | Next ]
 Jonathan Hoyle Posts: 398 Registered: 12/10/04
Re: ln(x^x)
Posted: May 9, 2000 4:12 PM

>> >I agree - of course ln(x^x) HAS an integral.
>> >

>> Does it have an integral for x<0 ?
>>

>
>First define it for x<0.

As long as we're at it, we could delve into complex analysis. The ln()
function (assuming the principle branch) is defined for all non-zero
complex values. Since z^z is non-zero for all non-zero z, we have
ln(z^z) = zln(z) defined for C \ {0}. Unfortunately, this function is
discontinuous for all z on the line x <= 0, just as ln(z) is.

Date Subject Author
5/6/00 \
5/6/00 Doug Norris
5/6/00 SirWobbly
5/8/00 anonymous
5/9/00 Didier Bizzarri
5/9/00 G. A. Edgar
5/9/00 anonymous
5/9/00 Jonathan Hoyle
5/9/00 Jonathan Hoyle
5/10/00 Robert Israel
5/6/00 Clive Tooth
5/6/00 J. Mayer
5/6/00 Fred W. Helenius
5/6/00 Doug Norris
5/6/00 Richard Carr
5/6/00 Doug Norris
5/9/00 Jonathan Hoyle
5/6/00 David Swanson
5/7/00 Herman Rubin
5/6/00 Stephen Norris
5/6/00 Zdislav V. Kovarik
5/7/00 Oscar Lanzi III
5/8/00 Bob Silverman