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Math Forum » Discussions » sci.math.* » sci.math.independent

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

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Jonathan Hoyle

Posts: 398
Registered: 12/10/04
Re: ln(x^x)
Posted: May 9, 2000 4:12 PM
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>> >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.

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