# lithium barbie doll

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 Apr23 asked Determining an Analytic Function from its Real Part Apr22 comment Show bounded harmonic function on $\mathbb{C}$ is constant.but how do we know that f is bounded? Only its real part is necessarily bounded. Apr22 revised Help me prove the identity $\overline{f(0)} = \frac{1}{2\pi}\int_0^{2\pi}\frac{e^{i\phi}}{e^{i \phi}-z}\overline{f(e^{i\phi})}d\phi$added 1 characters in body Apr22 comment Help me prove the identity $\overline{f(0)} = \frac{1}{2\pi}\int_0^{2\pi}\frac{e^{i\phi}}{e^{i \phi}-z}\overline{f(e^{i\phi})}d\phi$I agree, the integral always equaling the conjugate of f at a single point is for me a very counterintuitive. Apr22 revised Help me prove the identity $\overline{f(0)} = \frac{1}{2\pi}\int_0^{2\pi}\frac{e^{i\phi}}{e^{i \phi}-z}\overline{f(e^{i\phi})}d\phi$added 65 characters in body Apr22 answered Help me prove the identity $\overline{f(0)} = \frac{1}{2\pi}\int_0^{2\pi}\frac{e^{i\phi}}{e^{i \phi}-z}\overline{f(e^{i\phi})}d\phi$ Apr22 comment Help me prove the identity $\overline{f(0)} = \frac{1}{2\pi}\int_0^{2\pi}\frac{e^{i\phi}}{e^{i \phi}-z}\overline{f(e^{i\phi})}d\phi$You're right, my professor may have forgotten to stipulate that z be in the unit circle, since if it is I think I came up with a proof by expanding f as a power series centered at zero. Apr22 asked Help me prove the identity $\overline{f(0)} = \frac{1}{2\pi}\int_0^{2\pi}\frac{e^{i\phi}}{e^{i \phi}-z}\overline{f(e^{i\phi})}d\phi$ Apr21 comment Can someone check my work on this integral?log|z| has a singularity at zero, thus it's not holomorphic in a neighborhood containing our curve. Apr21 accepted Can someone check my work on this integral? Apr21 comment Can someone check my work on this integral?Ok cool, thanks anon. Apr21 asked Can someone check my work on this integral? Apr21 accepted A few Questions about Harmonic Functions Apr21 comment A few Questions about Harmonic FunctionsOk thanks Thomas, I'll take a look at this. Apr21 asked A few Questions about Harmonic Functions Apr21 accepted The Integral of a Harmonic Function Apr21 comment The Integral of a Harmonic FunctionGreat, thanks for the detailed response Zarrax! +1. Apr21 comment The Integral of a Harmonic FunctionCan you expand on this? Are you saying that the problem as stated is incorrect, and that I should switch the inequalities? Because that would make a lot more sense. Apr21 asked The Integral of a Harmonic Function Apr20 comment Show bounded harmonic function on $\mathbb{C}$ is constant.Are harmonic functions automatically analytic in $\mathbb{C}$? I was under the impression that they only necessarily have continuous partial derivatives satisfying the Laplacian.