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jtleafs33
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Homework Statement
Can a function which is purely real-valued be analytic? Describe the behavior of such functions?
Homework Equations
The Cauchy-Riemann conditions
ux=vy, vx=-uy
The Attempt at a Solution
I can't think of any pure real-valued equations off the top of my head which satisfy the CR conditions. However, could any function like sin(x), cos(x), e^x, which is infinitely differentiable be considered analytic? Doesn't infinite differentiability imply that the CR conditions are already satisfied?