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awwalker.com | ||
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mikespivey.wordpress.com
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| | | | | The Riemann zeta function $latex \zeta(s)$ can be expressed as $latex \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}$, for complex numbers s whose real part is greater than 1. By analytic continuation, $latex \zeta(s)$ can be extended to all complex numbers except where $latex s = 1$. The power sum $latex S_a(M)$ is given by $latex S_a(M) =... | |
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thatsmaths.com
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| | | | | The Riemann Hypothesis Perhaps the greatest unsolved problem in mathematics is to explain the distribution of the prime numbers. The overall ``thinning out'' of the primes less than some number $latex {N}&fg=000000$, as $latex {N}&fg=000000$ increases, is well understood, and is demonstrated by the Prime Number Theorem (PNT). In its simplest form, PNT states that... | |
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mattbaker.blog
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| | | | | On Pi Day 2016, I wrote inthis post about the remarkable fact, discovered by Euler, thatthe probability that two randomly chosen integers have no prime factors in common is $latex \frac{6}{\pi^2}$. The proof makes use of the famous identity $latex \sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$, often referred to as the "Basel problem", which is also due... | |
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statisticaloddsandends.wordpress.com
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| | | In this previous post, we defined Value at Risk (VaR): given a time horizon $latex T$ and a level $latex \alpha$, the VaR of an investment at level $latex \alpha$ over time horizon $latex T$ is a number or percentage X such that Over the time horizon $latex T$, the probability that the loss on... | ||
