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February 11th, 2015, 12:11 PM  #1 
Member Joined: Jul 2012 Posts: 60 Thanks: 0 Math Focus: Calculus  Analytic functions?
I am jumping into complex analysis, and getting really confused with some theory. So I get that a function is analytic when cauchyreimann rules apply (in almost all points) My question is, is there a shortcut to know when a function is analytic without differentiating? What if it's given as a function of z>f(z). Do I have to put in x+iy and then differentiate. Also can I get an example of a non analytic function. Also this is loosely tied to this topic, but could you throw in an example of a non harmonic function aswell? Thanks 
February 13th, 2015, 06:44 PM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 
There are a number of ways of defining "analytic function" but, honestly, the CauchyRiemann equations are the simplest way of determining whether or not a function is analytic. f(z)= z is neither analytic nor harmonic. f(z)= Re(z) and f(a)= Im(a) are other examples.


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