Talk:Holomorphic function
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the logarithm is holomorphic on the set {z not a non-negative real number}? is the correct? so the logarithm is not holomorphic on positive real numbers? that can't be right.....? perhaps it should read {z not a non-positive real number}? i.e. the logarithm is holomorphic on the positive reals, plus the complexes with nonzero imaginary part? -Lethe | Talk 22:15, Feb 11, 2004 (UTC)
- I think you're misreading. The log is holomorphic on the set C minus the subset z where z is a negative real. Maybe I'm misreading. The article could be more clear, for sure. 68.103.38.9 12:09, 23 Oct 2004 (UTC)
What is a seam?
This article says:
- The inverse trigonometric functions likewise have seams and are holomorphic everywhere except the seams.
Can some expert clarify what a seam is? Thanks! Oleg Alexandrov 06:10, 11 Feb 2005 (UTC)
- My motto is: When in doubt, cut it out.
- It is a small insignifcant fragment anyway. So what do you think? Oleg Alexandrov 02:14, 12 Feb 2005 (UTC)
"The limit here is taken over all sequences of complex numbers approaching z0," ?
Could someone explain what this means more precisely? Does "sequence" mean _Cauchy_ "sequence" here? (Also, what is the definition of a "Cauchy" sequence for complex numbers? Is does it just use the modulus for the "epsilon" in the epsilon-delta argument?).
- It means a sequence zn such that |zn-z0|→0 as n→∞. And about the definition of Cauchy sequences, you are right, you just use the complex modulus instead of the real modulus, everything else is the same as for sequences of real numbers. Oleg Alexandrov 18:30, 1 Mar 2005 (UTC)
I suppose the other way to define all this is by talking about the real and imaginary parts each converging to the real and imaginary parts of z0...
- Yes, this is another way of proceeding about it. Oleg Alexandrov 18:30, 1 Mar 2005 (UTC)
Either way... if someone could clarify this... it would be much appreciated (I am not a Math expert - stumbled across this trying to learn some calculus stuff).
- Do you still have questions about these? By the way, it is good to sign your comments, with four tildas ~~~~~. Cheers, Oleg Alexandrov 18:30, 1 Mar 2005 (UTC)