Consider the equation $$ \exp(- \sqrt{2 \log n} x_n - x_{n}^{2}/2) = (\sqrt{ 2 \log n} + x_n) \sqrt{2 \pi}. $$ What does it mean, that the leading terms for $x_n$ are given by $$ x_n = - \frac{\log \log n+ \log 4 \pi}{2 \sqrt{2 \log n}} $$ ?
2026-03-29 22:29:55.1774823395
Find $x_n$ such that $ \exp(- \sqrt{2 \log n} x_n - x_{n}^{2}/2) = (\sqrt{ 2 \log n} + x_n) \sqrt{2 \pi}$
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