I would like to find an analytic function $f=u+iv$ in $\Bbb C$ where $u=x^2-y^2-x$ and $f(z)|(z=0)=0$.
Finding an analytic function defined in the complex plane
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complex-analysis
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1Can you find an analytic $f_1$ whose real part is $x^2 - y^2$, and an analytic $f_2$ whose real part is $x$? Then $f = f_1 - f_2 + \operatorname{constant}$. – 2017-01-22
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0Thank you for your tip. Would $g(z)=z^2$ and $h(z)=z$ such that $f=g-h+constant$ be okay? – 2017-01-22
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0Should be $-h$, not $+h$. You now have your candidate, just check whether it does what is required. – 2017-01-22
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0Yes I have corrected it. Thank you very much. – 2017-01-22