I'm wondering if the following limit is nonzero; v E R
and if so, what is it equal to? Thanks
I know it doesn't converge for
and if so, what is it equal to? Thanks
I know it doesn't converge for
a curious limit

I'm wondering if the following limit is nonzero; v E R
and if so, what is it equal to? Thanks I know it doesn't converge for
04/14/2011, 08:10 PM
(This post was last modified: 04/14/2011, 08:11 PM by nuninho1980.)
attention: h > o is bad but yes h > 0. because 'o' isn't number and is letter. lol
04/14/2011, 08:21 PM
04/14/2011, 10:14 PM
(04/14/2011, 08:01 PM)JmsNxn Wrote: I'm wondering if the following limit is nonzero; v E R The powers with noninteger exponents are not uniquely defined in the complex plane. In your case you would need to put: But then the standard logarithm has a cut on , which is quite arbitrary: one could put a cut however one likes. For example could spiral around 0, while moving towards 0 and would increase/decrease its imaginary part by in each round. I guess it really depends on how approaches 0.
let's take the limit from positive (keep it simple first)
so: Is there any way of reexpressing this limit?
04/15/2011, 07:14 AM
04/15/2011, 05:09 PM
(04/15/2011, 07:14 AM)bo198214 Wrote: But then its not difficult, since on the reals, the whole limit goes to (complex) except for , for which the whole limit is 0. Alright, how about where is taken to mean approaching along the axis. I think it's the equivalent of: which I guess converges to negative infinity again, except for 1e^{vi}=0 hmm, seems this is less interesting than I thought.
04/16/2011, 07:22 PM
is there any way of letting h approach zero such that:
?
04/16/2011, 07:48 PM

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