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Complex Analytic Proof of the Gaussian Integral $\int_{-\infty}^{\infty}e^{-z^2}dz=\sqrt{\pi}$
4
Let $M$ be a maximal ideal in $R$ such that for all $x\in M$, $x+1$ is a unit. Show that $R$ is a local ring with maximal ideal $M$
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Accidents of small $n$
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Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$
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Help me prove the identity $\overline{f(0)} = \frac{1}{2\pi}\int_0^{2\pi}\frac{e^{i\phi}}{e^{i \phi}-z}\overline{f(e^{i\phi})}d\phi$
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