Let f(z) is be complex function and u(x,y) & v(x,y) be real functions.
f(z) is said to be holomorphic if u,v satisfy the Cauchy-Riemann equationspic.twitter.com/C0MPdaAg5w
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Interesting, I (mistakenly) thought the CR equations meant the function is analytic, which is not quite true, only holomorphic. I’ve had that wrong in my head for years!
I think the confusion honestly just comes from the fact that a lotttt of professors use them interchangeably.. though I’m certain my UG complex professor @rsachsgmu is certainly not to blame for my confusion
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Yeah, and for the most part, and especially as an UG in physics, we basically only work with analytic functions or assume them to be analytic.
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Just looked it up.. I’m confused again.. apparently they’re equivalent
End of conversation
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For single variable complex functions.. excuse me..I have some math grad students to yell at
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